---
_id: '55459'
article_type: original
author:
- first_name: Nils
  full_name: Bullerjahn, Nils
  id: '103797'
  last_name: Bullerjahn
  orcid: https://orcid.org/0009-0003-8460-1574
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Bullerjahn N, Kovács B. Error estimates for full discretization of Cahn--Hilliard
    equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>.
    doi:<a href="https://doi.org/10.1093/imanum/draf009">10.1093/imanum/draf009</a>
  apa: Bullerjahn, N., &#38; Kovács, B. (n.d.). Error estimates for full discretization
    of Cahn--Hilliard equation with dynamic boundary conditions. <i>IMA Journal of
    Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/draf009">https://doi.org/10.1093/imanum/draf009</a>
  bibtex: '@article{Bullerjahn_Kovács, title={Error estimates for full discretization
    of Cahn--Hilliard equation with dynamic boundary conditions}, DOI={<a href="https://doi.org/10.1093/imanum/draf009">10.1093/imanum/draf009</a>},
    journal={IMA Journal of Numerical Analysis}, author={Bullerjahn, Nils and Kovács,
    Balázs} }'
  chicago: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
    of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of
    Numerical Analysis</i>, n.d. <a href="https://doi.org/10.1093/imanum/draf009">https://doi.org/10.1093/imanum/draf009</a>.
  ieee: 'N. Bullerjahn and B. Kovács, “Error estimates for full discretization of
    Cahn--Hilliard equation with dynamic boundary conditions,” <i>IMA Journal of Numerical
    Analysis</i>, doi: <a href="https://doi.org/10.1093/imanum/draf009">10.1093/imanum/draf009</a>.'
  mla: Bullerjahn, Nils, and Balázs Kovács. “Error Estimates for Full Discretization
    of Cahn--Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of
    Numerical Analysis</i>, doi:<a href="https://doi.org/10.1093/imanum/draf009">10.1093/imanum/draf009</a>.
  short: N. Bullerjahn, B. Kovács, IMA Journal of Numerical Analysis (n.d.).
date_created: 2024-07-31T09:03:45Z
date_updated: 2026-02-18T14:46:18Z
department:
- _id: '841'
doi: 10.1093/imanum/draf009
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_status: accepted
status: public
title: Error estimates for full discretization of Cahn--Hilliard equation with dynamic
  boundary conditions
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '53141'
author:
- first_name: Dominik
  full_name: Edelmann, Dominik
  last_name: Edelmann
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Edelmann D, Kovács B, Lubich C. Numerical analysis of an evolving bulk--surface
    model of tumour growth. <i>IMA Journal of Numerical Analysis</i>. 2025;45(5):2581--2627.
    doi:<a href="https://doi.org/10.1093/imanum/drae077">10.1093/imanum/drae077</a>
  apa: Edelmann, D., Kovács, B., &#38; Lubich, C. (2025). Numerical analysis of an
    evolving bulk--surface model of tumour growth. <i>IMA Journal of Numerical Analysis</i>,
    <i>45</i>(5), 2581--2627. <a href="https://doi.org/10.1093/imanum/drae077">https://doi.org/10.1093/imanum/drae077</a>
  bibtex: '@article{Edelmann_Kovács_Lubich_2025, title={Numerical analysis of an evolving
    bulk--surface model of tumour growth}, volume={45}, DOI={<a href="https://doi.org/10.1093/imanum/drae077">10.1093/imanum/drae077</a>},
    number={5}, journal={IMA Journal of Numerical Analysis}, author={Edelmann, Dominik
    and Kovács, Balázs and Lubich, Christian}, year={2025}, pages={2581--2627} }'
  chicago: 'Edelmann, Dominik, Balázs Kovács, and Christian Lubich. “Numerical Analysis
    of an Evolving Bulk--Surface Model of Tumour Growth.” <i>IMA Journal of Numerical
    Analysis</i> 45, no. 5 (2025): 2581--2627. <a href="https://doi.org/10.1093/imanum/drae077">https://doi.org/10.1093/imanum/drae077</a>.'
  ieee: 'D. Edelmann, B. Kovács, and C. Lubich, “Numerical analysis of an evolving
    bulk--surface model of tumour growth,” <i>IMA Journal of Numerical Analysis</i>,
    vol. 45, no. 5, pp. 2581--2627, 2025, doi: <a href="https://doi.org/10.1093/imanum/drae077">10.1093/imanum/drae077</a>.'
  mla: Edelmann, Dominik, et al. “Numerical Analysis of an Evolving Bulk--Surface
    Model of Tumour Growth.” <i>IMA Journal of Numerical Analysis</i>, vol. 45, no.
    5, 2025, pp. 2581--2627, doi:<a href="https://doi.org/10.1093/imanum/drae077">10.1093/imanum/drae077</a>.
  short: D. Edelmann, B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 45 (2025)
    2581--2627.
date_created: 2024-04-03T09:11:36Z
date_updated: 2026-02-18T14:44:54Z
department:
- _id: '841'
doi: 10.1093/imanum/drae077
intvolume: '        45'
issue: '5'
language:
- iso: eng
page: 2581--2627
publication: IMA Journal of Numerical Analysis
status: public
title: Numerical analysis of an evolving bulk--surface model of tumour growth
type: journal_article
user_id: '100441'
volume: 45
year: '2025'
...
---
_id: '55781'
abstract:
- lang: eng
  text: "In this paper, we prove that spatially semi-discrete evolving finite element\r\nmethod
    for parabolic equations on a given evolving hypersurface of arbitrary\r\ndimensions
    preserves the maximal $L^p$-regularity at the discrete level. We\r\nfirst establish
    the results on a stationary surface and then extend them, via a\r\nperturbation
    argument, to the case where the underlying surface is evolving\r\nunder a prescribed
    velocity field. The proof combines techniques in evolving\r\nfinite element method,
    properties of Green's functions on (discretised) closed\r\nsurfaces, and local
    energy estimates for finite element methods"
author:
- first_name: Genming
  full_name: Bai, Genming
  last_name: Bai
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Buyang
  full_name: Li, Buyang
  last_name: Li
citation:
  ama: Bai G, Kovács B, Li B. Maximal regularity of evolving FEMs for parabolic equations
    on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>. Published online
    2025. doi:<a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a>
  apa: Bai, G., Kovács, B., &#38; Li, B. (2025). Maximal regularity of evolving FEMs
    for parabolic equations on an  evolving surface. <i>IMA Journal of Numerical Analysis</i>.
    <a href="https://doi.org/10.1093/imanum/draf082.">https://doi.org/10.1093/imanum/draf082.</a>
  bibtex: '@article{Bai_Kovács_Li_2025, title={Maximal regularity of evolving FEMs
    for parabolic equations on an  evolving surface}, DOI={<a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a>},
    journal={IMA Journal of Numerical Analysis}, author={Bai, Genming and Kovács,
    Balázs and Li, Buyang}, year={2025} }'
  chicago: Bai, Genming, Balázs Kovács, and Buyang Li. “Maximal Regularity of Evolving
    FEMs for Parabolic Equations on an  Evolving Surface.” <i>IMA Journal of Numerical
    Analysis</i>, 2025. <a href="https://doi.org/10.1093/imanum/draf082.">https://doi.org/10.1093/imanum/draf082.</a>
  ieee: 'G. Bai, B. Kovács, and B. Li, “Maximal regularity of evolving FEMs for parabolic
    equations on an  evolving surface,” <i>IMA Journal of Numerical Analysis</i>,
    2025, doi: <a href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a>'
  mla: Bai, Genming, et al. “Maximal Regularity of Evolving FEMs for Parabolic Equations
    on an  Evolving Surface.” <i>IMA Journal of Numerical Analysis</i>, 2025, doi:<a
    href="https://doi.org/10.1093/imanum/draf082.">10.1093/imanum/draf082.</a>
  short: G. Bai, B. Kovács, B. Li, IMA Journal of Numerical Analysis (2025).
date_created: 2024-08-27T07:37:39Z
date_updated: 2026-02-18T14:47:34Z
department:
- _id: '841'
doi: 10.1093/imanum/draf082.
external_id:
  arxiv:
  - '2408.14096'
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
status: public
title: Maximal regularity of evolving FEMs for parabolic equations on an  evolving
  surface
type: journal_article
user_id: '100441'
year: '2025'
...
---
_id: '45972'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Kovács B. Numerical surgery for mean curvature flow of surfaces. <i>SIAM Journal
    on Scientific Computing</i>. 2024;46(2):A645--A669. doi:<a href="https://doi.org/10.1137/22M1531919">10.1137/22M1531919</a>
  apa: Kovács, B. (2024). Numerical surgery for mean curvature flow of surfaces. <i>SIAM
    Journal on Scientific Computing</i>, <i>46</i>(2), A645--A669. <a href="https://doi.org/10.1137/22M1531919">https://doi.org/10.1137/22M1531919</a>
  bibtex: '@article{Kovács_2024, title={Numerical surgery for mean curvature flow
    of surfaces}, volume={46}, DOI={<a href="https://doi.org/10.1137/22M1531919">10.1137/22M1531919</a>},
    number={2}, journal={SIAM Journal on Scientific Computing}, author={Kovács, Balázs},
    year={2024}, pages={A645--A669} }'
  chicago: 'Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.”
    <i>SIAM Journal on Scientific Computing</i> 46, no. 2 (2024): A645--A669. <a href="https://doi.org/10.1137/22M1531919">https://doi.org/10.1137/22M1531919</a>.'
  ieee: 'B. Kovács, “Numerical surgery for mean curvature flow of surfaces,” <i>SIAM
    Journal on Scientific Computing</i>, vol. 46, no. 2, pp. A645--A669, 2024, doi:
    <a href="https://doi.org/10.1137/22M1531919">10.1137/22M1531919</a>.'
  mla: Kovács, Balázs. “Numerical Surgery for Mean Curvature Flow of Surfaces.” <i>SIAM
    Journal on Scientific Computing</i>, vol. 46, no. 2, 2024, pp. A645--A669, doi:<a
    href="https://doi.org/10.1137/22M1531919">10.1137/22M1531919</a>.
  short: B. Kovács, SIAM Journal on Scientific Computing 46 (2024) A645--A669.
date_created: 2023-07-10T12:32:34Z
date_updated: 2024-08-27T07:42:56Z
department:
- _id: '841'
doi: 10.1137/22M1531919
extern: '1'
intvolume: '        46'
issue: '2'
language:
- iso: eng
page: A645--A669
publication: SIAM Journal on Scientific Computing
status: public
title: Numerical surgery for mean curvature flow of surfaces
type: journal_article
user_id: '100441'
volume: 46
year: '2024'
...
---
_id: '55078'
abstract:
- lang: eng
  text: "This paper develops and discusses a residual-based a posteriori error\r\nestimate
    and a space--time adaptive algorithm for solving parabolic surface\r\npartial
    differential equations on closed stationary surfaces. The full\r\ndiscretization
    uses the surface finite element method in space and the backward\r\nEuler method
    in time. The proposed error indicator bounds the error quantities\r\nglobally
    in space from above and below, and globally in time from above and\r\nlocally
    from below. A space--time adaptive algorithm is proposed using the\r\nderived
    error indicator. Numerical experiments illustrate and complement the\r\ntheory."
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Michael Frederik Raúl
  full_name: Lantelme, Michael Frederik Raúl
  id: '102867'
  last_name: Lantelme
citation:
  ama: Kovács B, Lantelme MFR. A posteriori error estimates for parabolic partial
    differential equations on stationary surfaces. <i>arXiv:240702101</i>. Published
    online 2024.
  apa: Kovács, B., &#38; Lantelme, M. F. R. (2024). A posteriori error estimates for
    parabolic partial differential equations on stationary surfaces. In <i>arXiv:2407.02101</i>.
  bibtex: '@article{Kovács_Lantelme_2024, title={A posteriori error estimates for
    parabolic partial differential equations on stationary surfaces}, journal={arXiv:2407.02101},
    author={Kovács, Balázs and Lantelme, Michael Frederik Raúl}, year={2024} }'
  chicago: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error
    Estimates for Parabolic Partial Differential Equations on Stationary Surfaces.”
    <i>ArXiv:2407.02101</i>, 2024.
  ieee: B. Kovács and M. F. R. Lantelme, “A posteriori error estimates for parabolic
    partial differential equations on stationary surfaces,” <i>arXiv:2407.02101</i>.
    2024.
  mla: Kovács, Balázs, and Michael Frederik Raúl Lantelme. “A Posteriori Error Estimates
    for Parabolic Partial Differential Equations on Stationary Surfaces.” <i>ArXiv:2407.02101</i>,
    2024.
  short: B. Kovács, M.F.R. Lantelme, ArXiv:2407.02101 (2024).
date_created: 2024-07-04T12:53:47Z
date_updated: 2026-02-18T14:45:36Z
department:
- _id: '841'
external_id:
  arxiv:
  - '2407.02101'
language:
- iso: eng
publication: arXiv:2407.02101
status: public
title: A posteriori error estimates for parabolic partial differential equations on
  stationary surfaces
type: preprint
user_id: '100441'
year: '2024'
...
---
_id: '45971'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>An error estimate
    for a canonical discretization of the harmonic map heat flow into spheres is derived.
    The numerical scheme uses standard finite elements with a nodal treatment of linearized
    unit-length constraints. The analysis is based on elementary approximation results
    and only uses the discrete weak formulation.</jats:p>"
author:
- first_name: Sören
  full_name: Bartels, Sören
  last_name: Bartels
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Zhangxian
  full_name: Wang, Zhangxian
  last_name: Wang
citation:
  ama: Bartels S, Kovács B, Wang Z. Error analysis for the numerical approximation
    of the harmonic map heat flow with nodal constraints. <i>IMA Journal of Numerical
    Analysis</i>. Published online 2023. doi:<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>
  apa: Bartels, S., Kovács, B., &#38; Wang, Z. (2023). Error analysis for the numerical
    approximation of the harmonic map heat flow with nodal constraints. <i>IMA Journal
    of Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drad037">https://doi.org/10.1093/imanum/drad037</a>
  bibtex: '@article{Bartels_Kovács_Wang_2023, title={Error analysis for the numerical
    approximation of the harmonic map heat flow with nodal constraints}, DOI={<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Bartels, Sören and Kovács, Balázs and Wang, Zhangxian}, year={2023}
    }'
  chicago: Bartels, Sören, Balázs Kovács, and Zhangxian Wang. “Error Analysis for
    the Numerical Approximation of the Harmonic Map Heat Flow with Nodal Constraints.”
    <i>IMA Journal of Numerical Analysis</i>, 2023. <a href="https://doi.org/10.1093/imanum/drad037">https://doi.org/10.1093/imanum/drad037</a>.
  ieee: 'S. Bartels, B. Kovács, and Z. Wang, “Error analysis for the numerical approximation
    of the harmonic map heat flow with nodal constraints,” <i>IMA Journal of Numerical
    Analysis</i>, 2023, doi: <a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>.'
  mla: Bartels, Sören, et al. “Error Analysis for the Numerical Approximation of the
    Harmonic Map Heat Flow with Nodal Constraints.” <i>IMA Journal of Numerical Analysis</i>,
    Oxford University Press (OUP), 2023, doi:<a href="https://doi.org/10.1093/imanum/drad037">10.1093/imanum/drad037</a>.
  short: S. Bartels, B. Kovács, Z. Wang, IMA Journal of Numerical Analysis (2023).
date_created: 2023-07-10T12:32:10Z
date_updated: 2024-04-03T09:15:27Z
department:
- _id: '841'
doi: 10.1093/imanum/drad037
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error analysis for the numerical approximation of the harmonic map heat flow
  with nodal constraints
type: journal_article
user_id: '100441'
year: '2023'
...
---
_id: '53140'
abstract:
- lang: eng
  text: We present a new stability and error analysis of fully discrete approximation
    schemes for the transient Stokes equation. For the spatial discretization, we
    consider a wide class of Galerkin finite element methods which includes both inf-sup
    stable spaces and symmetric pressure stabilized formulations. We extend the results
    from Burman and Fernández [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439]
    and provide a unified theoretical analysis of backward difference formulae (BDF
    methods) of order 1 to 6. The main novelty of our approach lies in the use of
    Dahlquist's G-stability concept together with multiplier techniques introduced
    by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.},
    59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for
    both the velocity and the pressure. When combined with a method dependent Ritz
    projection for the initial data, unconditional stability can be shown while for
    arbitrary interpolation, pressure stability is subordinate to the fulfillment
    of a mild inverse CFL-type condition between space and time discretizations.
author:
- first_name: Alessandro
  full_name: Contri, Alessandro
  last_name: Contri
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: André
  full_name: Massing, André
  last_name: Massing
citation:
  ama: 'Contri A, Kovács B, Massing A. Error analysis of BDF 1-6 time-stepping methods
    for the transient Stokes problem: velocity and pressure estimates. <i>arXiv</i>.
    Published online 2023. doi:<a href="https://doi.org/10.48550/ARXIV.2312.05511">10.48550/ARXIV.2312.05511</a>'
  apa: 'Contri, A., Kovács, B., &#38; Massing, A. (2023). Error analysis of BDF 1-6
    time-stepping methods for the transient Stokes problem: velocity and pressure
    estimates. <i>ArXiv</i>. <a href="https://doi.org/10.48550/ARXIV.2312.05511">https://doi.org/10.48550/ARXIV.2312.05511</a>'
  bibtex: '@article{Contri_Kovács_Massing_2023, title={Error analysis of BDF 1-6 time-stepping
    methods for the transient Stokes problem: velocity and pressure estimates}, DOI={<a
    href="https://doi.org/10.48550/ARXIV.2312.05511">10.48550/ARXIV.2312.05511</a>},
    journal={arXiv}, author={Contri, Alessandro and Kovács, Balázs and Massing, André},
    year={2023} }'
  chicago: 'Contri, Alessandro, Balázs Kovács, and André Massing. “Error Analysis
    of BDF 1-6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and
    Pressure Estimates.” <i>ArXiv</i>, 2023. <a href="https://doi.org/10.48550/ARXIV.2312.05511">https://doi.org/10.48550/ARXIV.2312.05511</a>.'
  ieee: 'A. Contri, B. Kovács, and A. Massing, “Error analysis of BDF 1-6 time-stepping
    methods for the transient Stokes problem: velocity and pressure estimates,” <i>arXiv</i>,
    2023, doi: <a href="https://doi.org/10.48550/ARXIV.2312.05511">10.48550/ARXIV.2312.05511</a>.'
  mla: 'Contri, Alessandro, et al. “Error Analysis of BDF 1-6 Time-Stepping Methods
    for the Transient Stokes Problem: Velocity and Pressure Estimates.” <i>ArXiv</i>,
    2023, doi:<a href="https://doi.org/10.48550/ARXIV.2312.05511">10.48550/ARXIV.2312.05511</a>.'
  short: A. Contri, B. Kovács, A. Massing, ArXiv (2023).
date_created: 2024-04-03T09:08:38Z
date_updated: 2024-04-03T09:12:47Z
department:
- _id: '841'
doi: 10.48550/ARXIV.2312.05511
language:
- iso: eng
publication: arXiv
status: public
title: 'Error analysis of BDF 1-6 time-stepping methods for the transient Stokes problem:
  velocity and pressure estimates'
type: journal_article
user_id: '100441'
year: '2023'
...
---
_id: '45970'
abstract:
- lang: eng
  text: '<jats:p> We introduce a new phase field model for tumor growth where viscoelastic
    effects are taken into account. The model is derived from basic thermodynamical
    principles and consists of a convected Cahn–Hilliard equation with source terms
    for the tumor cells and a convected reaction–diffusion equation with boundary
    supply for the nutrient. Chemotactic terms, which are essential for the invasive
    behavior of tumors, are taken into account. The model is completed by a viscoelastic
    system consisting of the Navier–Stokes equation for the hydrodynamic quantities,
    and a general constitutive equation with stress relaxation for the left Cauchy–Green
    tensor associated with the elastic part of the total mechanical response of the
    viscoelastic material. For a specific choice of the elastic energy density and
    with an additional dissipative term accounting for stress diffusion, we prove
    existence of global-in-time weak solutions of the viscoelastic model for tumor
    growth in two space dimensions [Formula: see text] by the passage to the limit
    in a fully-discrete finite element scheme where a CFL condition, i.e. [Formula:
    see text], is required. </jats:p><jats:p> Moreover, in arbitrary dimensions [Formula:
    see text], we show stability and existence of solutions for the fully-discrete
    finite element scheme, where positive definiteness of the discrete Cauchy–Green
    tensor is proved with a regularization technique that was first introduced by
    Barrett and Boyaval [Existence and approximation of a (regularized) Oldroyd-B
    model, Math. Models Methods Appl. Sci. 21 (2011) 1783–1837]. After that, we improve
    the regularity results in arbitrary dimensions [Formula: see text] and in two
    dimensions [Formula: see text], where a CFL condition is required. Then, in two
    dimensions [Formula: see text], we pass to the limit in the discretization parameters
    and show that subsequences of discrete solutions converge to a global-in-time
    weak solution. Finally, we present numerical results in two dimensions [Formula:
    see text]. </jats:p>'
author:
- first_name: Harald
  full_name: Garcke, Harald
  last_name: Garcke
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Dennis
  full_name: Trautwein, Dennis
  last_name: Trautwein
citation:
  ama: Garcke H, Kovács B, Trautwein D. Viscoelastic Cahn–Hilliard models for tumor
    growth. <i>Mathematical Models and Methods in Applied Sciences</i>. 2022;32(13):2673-2758.
    doi:<a href="https://doi.org/10.1142/s0218202522500634">10.1142/s0218202522500634</a>
  apa: Garcke, H., Kovács, B., &#38; Trautwein, D. (2022). Viscoelastic Cahn–Hilliard
    models for tumor growth. <i>Mathematical Models and Methods in Applied Sciences</i>,
    <i>32</i>(13), 2673–2758. <a href="https://doi.org/10.1142/s0218202522500634">https://doi.org/10.1142/s0218202522500634</a>
  bibtex: '@article{Garcke_Kovács_Trautwein_2022, title={Viscoelastic Cahn–Hilliard
    models for tumor growth}, volume={32}, DOI={<a href="https://doi.org/10.1142/s0218202522500634">10.1142/s0218202522500634</a>},
    number={13}, journal={Mathematical Models and Methods in Applied Sciences}, publisher={World
    Scientific Pub Co Pte Ltd}, author={Garcke, Harald and Kovács, Balázs and Trautwein,
    Dennis}, year={2022}, pages={2673–2758} }'
  chicago: 'Garcke, Harald, Balázs Kovács, and Dennis Trautwein. “Viscoelastic Cahn–Hilliard
    Models for Tumor Growth.” <i>Mathematical Models and Methods in Applied Sciences</i>
    32, no. 13 (2022): 2673–2758. <a href="https://doi.org/10.1142/s0218202522500634">https://doi.org/10.1142/s0218202522500634</a>.'
  ieee: 'H. Garcke, B. Kovács, and D. Trautwein, “Viscoelastic Cahn–Hilliard models
    for tumor growth,” <i>Mathematical Models and Methods in Applied Sciences</i>,
    vol. 32, no. 13, pp. 2673–2758, 2022, doi: <a href="https://doi.org/10.1142/s0218202522500634">10.1142/s0218202522500634</a>.'
  mla: Garcke, Harald, et al. “Viscoelastic Cahn–Hilliard Models for Tumor Growth.”
    <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 32, no. 13, World
    Scientific Pub Co Pte Ltd, 2022, pp. 2673–758, doi:<a href="https://doi.org/10.1142/s0218202522500634">10.1142/s0218202522500634</a>.
  short: H. Garcke, B. Kovács, D. Trautwein, Mathematical Models and Methods in Applied
    Sciences 32 (2022) 2673–2758.
date_created: 2023-07-10T11:47:27Z
date_updated: 2024-04-03T09:15:35Z
department:
- _id: '841'
doi: 10.1142/s0218202522500634
intvolume: '        32'
issue: '13'
keyword:
- Applied Mathematics
- Modeling and Simulation
language:
- iso: eng
page: 2673-2758
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
  issn:
  - 0218-2025
  - 1793-6314
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: Viscoelastic Cahn–Hilliard models for tumor growth
type: journal_article
user_id: '100441'
volume: 32
year: '2022'
...
---
_id: '45969'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>An evolving surface finite element
    discretisation is analysed for the evolution of a closed two-dimensional surface
    governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion
    process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms
    are proposed, both based on a system coupling the diffusion equation to evolution
    equations for geometric quantities in the velocity law for the surface. One of
    the numerical methods is proved to be convergent in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$</jats:tex-math><mml:math
    xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>norm
    with optimal-order for finite elements of degree at least two. We present numerical
    experiments illustrating the convergence behaviour and demonstrating the qualitative
    properties of the flow: preservation of mean convexity, loss of convexity, weak
    maximum principles, and the occurrence of self-intersections.</jats:p>'
author:
- first_name: Charles M.
  full_name: Elliott, Charles M.
  last_name: Elliott
- first_name: Harald
  full_name: Garcke, Harald
  last_name: Garcke
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean
    curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>.
    2022;151(4):873-925. doi:<a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>
  apa: Elliott, C. M., Garcke, H., &#38; Kovács, B. (2022). Numerical analysis for
    the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische
    Mathematik</i>, <i>151</i>(4), 873–925. <a href="https://doi.org/10.1007/s00211-022-01301-3">https://doi.org/10.1007/s00211-022-01301-3</a>
  bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
    interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
    DOI={<a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs},
    year={2022}, pages={873–925} }'
  chicago: 'Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis
    for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.”
    <i>Numerische Mathematik</i> 151, no. 4 (2022): 873–925. <a href="https://doi.org/10.1007/s00211-022-01301-3">https://doi.org/10.1007/s00211-022-01301-3</a>.'
  ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
    of mean curvature flow and diffusion on closed surfaces,” <i>Numerische Mathematik</i>,
    vol. 151, no. 4, pp. 873–925, 2022, doi: <a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>.'
  mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
    Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i>,
    vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:<a
    href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>.
  short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.
date_created: 2023-07-10T11:47:11Z
date_updated: 2024-04-03T09:15:44Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01301-3
intvolume: '       151'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 873-925
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Numerical analysis for the interaction of mean curvature flow and diffusion
  on closed surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45963'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The scattering of electromagnetic
    waves from obstacles with wave-material interaction in thin layers on the surface
    is described by generalized impedance boundary conditions, which provide effective
    approximate models. In particular, this includes a thin coating around a perfect
    conductor and the skin effect of a highly conducting material. The approach taken
    in this work is to derive, analyse and discretize a system of time-dependent boundary
    integral equations that determines the tangential traces of the scattered electric
    and magnetic fields. In a familiar second step, the fields are evaluated in the
    exterior domain by a representation formula, which uses the time-dependent potential
    operators of Maxwell’s equations. The time-dependent boundary integral equation
    is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas
    boundary elements in space. Using the frequency-explicit bounds from the well-posedness
    analysis given here together with known approximation properties of the numerical
    methods, the full discretization is proved to be stable and convergent, with explicitly
    given rates in the case of sufficient regularity. Taking the same Runge–Kutta
    based convolution quadrature for discretizing the time-dependent representation
    formulas, the optimal order of convergence is obtained away from the scattering
    boundary, whereas an order reduction occurs close to the boundary. The theoretical
    results are illustrated by numerical experiments.</jats:p>
author:
- first_name: Jörg
  full_name: Nick, Jörg
  last_name: Nick
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from
    thin layers. <i>Numerische Mathematik</i>. 2022;150(4):1123-1164. doi:<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>
  apa: Nick, J., Kovács, B., &#38; Lubich, C. (2022). Time-dependent electromagnetic
    scattering from thin layers. <i>Numerische Mathematik</i>, <i>150</i>(4), 1123–1164.
    <a href="https://doi.org/10.1007/s00211-022-01277-0">https://doi.org/10.1007/s00211-022-01277-0</a>
  bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
    scattering from thin layers}, volume={150}, DOI={<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022},
    pages={1123–1164} }'
  chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic
    Scattering from Thin Layers.” <i>Numerische Mathematik</i> 150, no. 4 (2022):
    1123–64. <a href="https://doi.org/10.1007/s00211-022-01277-0">https://doi.org/10.1007/s00211-022-01277-0</a>.'
  ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
    from thin layers,” <i>Numerische Mathematik</i>, vol. 150, no. 4, pp. 1123–1164,
    2022, doi: <a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>.'
  mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
    <i>Numerische Mathematik</i>, vol. 150, no. 4, Springer Science and Business Media
    LLC, 2022, pp. 1123–64, doi:<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>.
  short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: '       150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45964'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>Maximal parabolic
    $L^p$-regularity of linear parabolic equations on an evolving surface is shown
    by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
    on a fixed surface. By freezing the coefficients in the parabolic equations at
    a fixed time and utilizing a perturbation argument around the freezed time, it
    is shown that backward difference time discretizations of linear parabolic equations
    on an evolving surface along characteristic trajectories can preserve maximal
    $L^p$-regularity in the discrete setting. The result is applied to prove the stability
    and convergence of time discretizations of nonlinear parabolic equations on an
    evolving surface, with linearly implicit backward differentiation formulae characteristic
    trajectories of the surface, for general locally Lipschitz nonlinearities. The
    discrete maximal $L^p$-regularity is used to prove the boundedness and stability
    of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
    used to bound the nonlinear terms in the stability analysis. Optimal-order error
    estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
    is obtained by combining the stability analysis with the consistency estimates.</jats:p>"
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Buyang
  full_name: Li, Buyang
  last_name: Li
citation:
  ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
    for evolving surface PDEs and its application to nonlinear problems. <i>IMA Journal
    of Numerical Analysis</i>. Published online 2022. doi:<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>
  apa: Kovács, B., &#38; Li, B. (2022). Maximal regularity of backward difference
    time discretization for evolving surface PDEs and its application to nonlinear
    problems. <i>IMA Journal of Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drac033">https://doi.org/10.1093/imanum/drac033</a>
  bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
    time discretization for evolving surface PDEs and its application to nonlinear
    problems}, DOI={<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
  chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
    Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
    Problems.” <i>IMA Journal of Numerical Analysis</i>, 2022. <a href="https://doi.org/10.1093/imanum/drac033">https://doi.org/10.1093/imanum/drac033</a>.
  ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
    for evolving surface PDEs and its application to nonlinear problems,” <i>IMA Journal
    of Numerical Analysis</i>, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>.'
  mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
    Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
    <i>IMA Journal of Numerical Analysis</i>, Oxford University Press (OUP), 2022,
    doi:<a href="https://doi.org/10.1093/imanum/drac033">10.1093/imanum/drac033</a>.
  short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
  surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>This paper studies
    bulk–surface splitting methods of first order for (semilinear) parabolic partial
    differential equations with dynamic boundary conditions. The proposed Lie splitting
    scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
    equation system, i.e., the boundary conditions are considered as a second dynamic
    equation that is coupled to the bulk problem. The splitting approach is combined
    with bulk–surface finite elements and an implicit Euler discretization of the
    two subsystems. We prove first-order convergence of the resulting fully discrete
    scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
    h$ for some constant $c&amp;gt;0$. The convergence is also illustrated numerically
    using dynamic boundary conditions of Allen–Cahn type.</jats:p>"
author:
- first_name: Robert
  full_name: Altmann, Robert
  last_name: Altmann
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christoph
  full_name: Zimmer, Christoph
  last_name: Zimmer
citation:
  ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
    with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2022;43(2):950-975.
    doi:<a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>
  apa: Altmann, R., Kovács, B., &#38; Zimmer, C. (2022). Bulk–surface Lie splitting
    for parabolic problems with dynamic boundary conditions. <i>IMA Journal of Numerical
    Analysis</i>, <i>43</i>(2), 950–975. <a href="https://doi.org/10.1093/imanum/drac002">https://doi.org/10.1093/imanum/drac002</a>
  bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
    for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={<a
    href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>}, number={2},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
    pages={950–975} }'
  chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
    Splitting for Parabolic Problems with Dynamic Boundary Conditions.” <i>IMA Journal
    of Numerical Analysis</i> 43, no. 2 (2022): 950–75. <a href="https://doi.org/10.1093/imanum/drac002">https://doi.org/10.1093/imanum/drac002</a>.'
  ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
    problems with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>,
    vol. 43, no. 2, pp. 950–975, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>.'
  mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
    with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol.
    43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:<a href="https://doi.org/10.1093/imanum/drac002">10.1093/imanum/drac002</a>.
  short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
    950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: '        43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>We derive a numerical
    method, based on operator splitting, to abstract parabolic semilinear boundary
    coupled systems. The method decouples the linear components that describe the
    coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
    the nonlinear terms similarly to an exponential integrator. The convergence proof
    is based on estimates for a recursive formulation of the error, using the parabolic
    smoothing property of analytic semigroups, and a careful comparison of the exact
    and approximate flows. This analysis also requires a deep understanding of the
    effects of the Dirichlet operator (the abstract version of the harmonic extension
    operator), which is essential for the stable coupling in our method. Numerical
    experiments, including problems with dynamic boundary conditions, reporting on
    convergence rates are presented.</jats:p>"
author:
- first_name: Petra
  full_name: Csomós, Petra
  last_name: Csomós
- first_name: Bálint
  full_name: Farkas, Bálint
  last_name: Farkas
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
    abstract semilinear boundary coupled systems. <i>IMA Journal of Numerical Analysis</i>.
    Published online 2022. doi:<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>
  apa: Csomós, P., Farkas, B., &#38; Kovács, B. (2022). Error estimates for a splitting
    integrator for abstract semilinear boundary coupled systems. <i>IMA Journal of
    Numerical Analysis</i>. <a href="https://doi.org/10.1093/imanum/drac079">https://doi.org/10.1093/imanum/drac079</a>
  bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
    integrator for abstract semilinear boundary coupled systems}, DOI={<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
    }'
  chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
    Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” <i>IMA
    Journal of Numerical Analysis</i>, 2022. <a href="https://doi.org/10.1093/imanum/drac079">https://doi.org/10.1093/imanum/drac079</a>.
  ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
    for abstract semilinear boundary coupled systems,” <i>IMA Journal of Numerical
    Analysis</i>, 2022, doi: <a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>.'
  mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
    Semilinear Boundary Coupled Systems.” <i>IMA Journal of Numerical Analysis</i>,
    Oxford University Press (OUP), 2022, doi:<a href="https://doi.org/10.1093/imanum/drac079">10.1093/imanum/drac079</a>.
  short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
  coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In this paper, we consider a non-linear
    fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with
    prescribed velocity, where the non-linear terms are only assumed to have locally
    Lipschitz derivatives. High-order evolving surface finite elements are used to
    discretise the weak equation system in space, and a modified matrix–vector formulation
    for the semi-discrete problem is derived. The anti-symmetric structure of the
    equation system is preserved by the spatial discretisation. A new stability proof,
    based on this structure, combined with consistency bounds proves optimal-order
    and uniform-in-time error estimates. The paper is concluded by a variety of numerical
    experiments.</jats:p>
author:
- first_name: Cedric Aaron
  full_name: Beschle, Cedric Aaron
  last_name: Beschle
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type
    equations on evolving surfaces. <i>Numerische Mathematik</i>. 2022;151(1):1-48.
    doi:<a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>
  apa: Beschle, C. A., &#38; Kovács, B. (2022). Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>,
    <i>151</i>(1), 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>
  bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>},
    number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48}
    }'
  chicago: 'Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates
    for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische
    Mathematik</i> 151, no. 1 (2022): 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>.'
  ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
    Cahn–Hilliard-type equations on evolving surfaces,” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, pp. 1–48, 2022, doi: <a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.'
  mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
    Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.
  short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: '       151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
  evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45956'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>The full Maxwell
    equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert
    equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose
    a weak formulation of the coupled system based on the boundary integral formulation
    of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness
    of a weak solution and propose a new numerical algorithm based on finite elements
    and boundary elements as spatial discretization with backward Euler and convolution
    quadrature for the time domain.\r\nThis is the first numerical algorithm which
    is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and
    full Maxwell’s equations without any simplifications like quasi-static approximations
    (e.g. eddy current model) and without restrictions on the shape of the domain
    (e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm
    under minimal assumptions on the regularity of the solution.\r\nThis is particularly
    important as there are few regularity results available and one generally expects
    the solution to be non-smooth.\r\nNumerical experiments illustrate and expand
    on the theoretical results.</jats:p>"
author:
- first_name: Jan
  full_name: Bohn, Jan
  last_name: Bohn
- first_name: Michael
  full_name: Feischl, Michael
  last_name: Feischl
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: 'Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational
    Methods in Applied Mathematics</i>. 2022;23(1):19-48. doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>'
  apa: 'Bohn, J., Feischl, M., &#38; Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational
    Methods in Applied Mathematics</i>, <i>23</i>(1), 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a>'
  bibtex: '@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation},
    volume={23}, DOI={<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>},
    number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
    de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs},
    year={2022}, pages={19–48} }'
  chicago: 'Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the
    Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form
    and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i>
    23, no. 1 (2022): 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a>.'
  ieee: 'J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation,”
    <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, pp. 19–48,
    2022, doi: <a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>.'
  mla: 'Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
    Equations via Convolution Quadrature: Weak Form and Numerical Approximation.”
    <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, Walter de
    Gruyter GmbH, 2022, pp. 19–48, doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>.'
  short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics
    23 (2022) 19–48.
date_created: 2023-07-10T11:43:13Z
date_updated: 2024-04-03T09:20:30Z
department:
- _id: '841'
doi: 10.1515/cmam-2022-0145
intvolume: '        23'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
language:
- iso: eng
page: 19-48
publication: Computational Methods in Applied Mathematics
publication_identifier:
  issn:
  - 1609-4840
  - 1609-9389
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution
  Quadrature: Weak Form and Numerical Approximation'
type: journal_article
user_id: '100441'
volume: 23
year: '2022'
...
---
_id: '45967'
author:
- first_name: Tim
  full_name: Binz, Tim
  last_name: Binz
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Binz T, Kovács B. A convergent finite element algorithm for mean curvature
    flow in higher codimension. <i>arXiv</i>. Published online 2021.
  apa: Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for
    mean curvature flow in higher codimension. <i>ArXiv</i>.
  bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
    for mean curvature flow in higher codimension}, journal={arXiv}, author={Binz,
    Tim and Kovács, Balázs}, year={2021} }'
  chicago: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for
    Mean Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.
  ieee: T. Binz and B. Kovács, “A convergent finite element algorithm for mean curvature
    flow in higher codimension,” <i>arXiv</i>, 2021.
  mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean
    Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.
  short: T. Binz, B. Kovács, ArXiv (2021).
date_created: 2023-07-10T11:46:16Z
date_updated: 2024-04-03T09:16:19Z
department:
- _id: '841'
language:
- iso: eng
publication: arXiv
status: public
title: A convergent finite element algorithm for mean curvature flow in higher codimension
type: journal_article
user_id: '100441'
year: '2021'
...
---
_id: '45962'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>An algorithm
    is proposed for generalized mean curvature flow of closed two-dimensional surfaces,
    which include inverse mean curvature flow and powers of mean and inverse mean
    curvature flow. Error estimates are proved for semidiscretizations and full discretizations
    for the generalized flow. The algorithm proposed and studied here combines evolving
    surface finite elements, whose nodes determine the discrete surface, and linearly
    implicit backward difference formulae for time integration. The numerical method
    is based on a system coupling the surface evolution to nonlinear second-order
    parabolic evolution equations for the normal velocity and normal vector. A convergence
    proof is presented in the case of finite elements of polynomial degree at least
    2 and backward difference formulae of orders 2 to 5. The error analysis combines
    stability estimates and consistency estimates to yield optimal-order $H^1$-norm
    error bounds for the computed surface position, velocity, normal vector, normal
    velocity and therefore for the mean curvature. The stability analysis is performed
    in the matrix–vector formulation and is independent of geometric arguments, which
    only enter the consistency analysis. Numerical experiments are presented to illustrate
    the convergence results and also to report on monotone quantities, e.g. Hawking
    mass for inverse mean curvature flow, and complemented by experiments for nonconvex
    surfaces.</jats:p>"
author:
- first_name: Tim
  full_name: Binz, Tim
  last_name: Binz
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Binz T, Kovács B. A convergent finite element algorithm for generalized mean
    curvature flows of closed surfaces. <i>IMA Journal of Numerical Analysis</i>.
    2021;42(3):2545-2588. doi:<a href="https://doi.org/10.1093/imanum/drab043">10.1093/imanum/drab043</a>
  apa: Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for
    generalized mean curvature flows of closed surfaces. <i>IMA Journal of Numerical
    Analysis</i>, <i>42</i>(3), 2545–2588. <a href="https://doi.org/10.1093/imanum/drab043">https://doi.org/10.1093/imanum/drab043</a>
  bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
    for generalized mean curvature flows of closed surfaces}, volume={42}, DOI={<a
    href="https://doi.org/10.1093/imanum/drab043">10.1093/imanum/drab043</a>}, number={3},
    journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
    (OUP)}, author={Binz, Tim and Kovács, Balázs}, year={2021}, pages={2545–2588}
    }'
  chicago: 'Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for
    Generalized Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical
    Analysis</i> 42, no. 3 (2021): 2545–88. <a href="https://doi.org/10.1093/imanum/drab043">https://doi.org/10.1093/imanum/drab043</a>.'
  ieee: 'T. Binz and B. Kovács, “A convergent finite element algorithm for generalized
    mean curvature flows of closed surfaces,” <i>IMA Journal of Numerical Analysis</i>,
    vol. 42, no. 3, pp. 2545–2588, 2021, doi: <a href="https://doi.org/10.1093/imanum/drab043">10.1093/imanum/drab043</a>.'
  mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized
    Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical Analysis</i>,
    vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2545–88, doi:<a href="https://doi.org/10.1093/imanum/drab043">10.1093/imanum/drab043</a>.
  short: T. Binz, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2545–2588.
date_created: 2023-07-10T11:44:41Z
date_updated: 2024-04-03T09:18:40Z
department:
- _id: '841'
doi: 10.1093/imanum/drab043
intvolume: '        42'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 2545-2588
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: A convergent finite element algorithm for generalized mean curvature flows
  of closed surfaces
type: journal_article
user_id: '100441'
volume: 42
year: '2021'
...
---
_id: '45957'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for
    a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation
    with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation
    is studied in an abstract weak formulation as a second-order system. Optimal-order
    uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error
    estimates are based on a consistency and stability analysis. The proof of stability
    is performed in an abstract framework, based on energy estimates exploiting the
    anti-symmetric structure of the second-order system. Numerical experiments illustrate
    the theoretical results.</jats:p>
author:
- first_name: Paula
  full_name: Harder, Paula
  last_name: Harder
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Harder P, Kovács B. Error estimates for the Cahn–Hilliard equation with dynamic
    boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2021;42(3):2589-2620.
    doi:<a href="https://doi.org/10.1093/imanum/drab045">10.1093/imanum/drab045</a>
  apa: Harder, P., &#38; Kovács, B. (2021). Error estimates for the Cahn–Hilliard
    equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>,
    <i>42</i>(3), 2589–2620. <a href="https://doi.org/10.1093/imanum/drab045">https://doi.org/10.1093/imanum/drab045</a>
  bibtex: '@article{Harder_Kovács_2021, title={Error estimates for the Cahn–Hilliard
    equation with dynamic boundary conditions}, volume={42}, DOI={<a href="https://doi.org/10.1093/imanum/drab045">10.1093/imanum/drab045</a>},
    number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Harder, Paula and Kovács, Balázs}, year={2021}, pages={2589–2620}
    }'
  chicago: 'Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard
    Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>
    42, no. 3 (2021): 2589–2620. <a href="https://doi.org/10.1093/imanum/drab045">https://doi.org/10.1093/imanum/drab045</a>.'
  ieee: 'P. Harder and B. Kovács, “Error estimates for the Cahn–Hilliard equation
    with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol.
    42, no. 3, pp. 2589–2620, 2021, doi: <a href="https://doi.org/10.1093/imanum/drab045">10.1093/imanum/drab045</a>.'
  mla: Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation
    with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol.
    42, no. 3, Oxford University Press (OUP), 2021, pp. 2589–620, doi:<a href="https://doi.org/10.1093/imanum/drab045">10.1093/imanum/drab045</a>.
  short: P. Harder, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2589–2620.
date_created: 2023-07-10T11:43:28Z
date_updated: 2024-04-03T09:20:15Z
department:
- _id: '841'
doi: 10.1093/imanum/drab045
intvolume: '        42'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 2589-2620
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 42
year: '2021'
...
---
_id: '45961'
author:
- first_name: Jörg
  full_name: Nick, Jörg
  last_name: Nick
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: 'Nick J, Kovács B, Lubich C. Correction to: Stable and convergent fully discrete
    interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>.
    2021;147(4):997-1000. doi:<a href="https://doi.org/10.1007/s00211-021-01196-6">10.1007/s00211-021-01196-6</a>'
  apa: 'Nick, J., Kovács, B., &#38; Lubich, C. (2021). Correction to: Stable and convergent
    fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische
    Mathematik</i>, <i>147</i>(4), 997–1000. <a href="https://doi.org/10.1007/s00211-021-01196-6">https://doi.org/10.1007/s00211-021-01196-6</a>'
  bibtex: '@article{Nick_Kovács_Lubich_2021, title={Correction to: Stable and convergent
    fully discrete interior–exterior coupling of Maxwell’s equations}, volume={147},
    DOI={<a href="https://doi.org/10.1007/s00211-021-01196-6">10.1007/s00211-021-01196-6</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2021},
    pages={997–1000} }'
  chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Correction to: Stable
    and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.”
    <i>Numerische Mathematik</i> 147, no. 4 (2021): 997–1000. <a href="https://doi.org/10.1007/s00211-021-01196-6">https://doi.org/10.1007/s00211-021-01196-6</a>.'
  ieee: 'J. Nick, B. Kovács, and C. Lubich, “Correction to: Stable and convergent
    fully discrete interior–exterior coupling of Maxwell’s equations,” <i>Numerische
    Mathematik</i>, vol. 147, no. 4, pp. 997–1000, 2021, doi: <a href="https://doi.org/10.1007/s00211-021-01196-6">10.1007/s00211-021-01196-6</a>.'
  mla: 'Nick, Jörg, et al. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior
    Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>, vol. 147, no.
    4, Springer Science and Business Media LLC, 2021, pp. 997–1000, doi:<a href="https://doi.org/10.1007/s00211-021-01196-6">10.1007/s00211-021-01196-6</a>.'
  short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 147 (2021) 997–1000.
date_created: 2023-07-10T11:44:25Z
date_updated: 2024-04-03T09:18:52Z
department:
- _id: '841'
doi: 10.1007/s00211-021-01196-6
intvolume: '       147'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 997-1000
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: 'Correction to: Stable and convergent fully discrete interior–exterior coupling
  of Maxwell’s equations'
type: journal_article
user_id: '100441'
volume: 147
year: '2021'
...
---
_id: '45953'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>$L^2$ norm error
    estimates of semi- and full discretizations of wave equations with dynamic boundary
    conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied.
    The analysis rests on an abstract formulation and error estimates, via energy
    techniques, within this abstract setting. Four prototypical linear wave equations
    with dynamic boundary conditions are analysed, which fit into the abstract framework.
    For problems with velocity terms or with acoustic boundary conditions we prove
    surprising results: for such problems the spatial convergence order is shown to
    be less than 2. These can also be observed in the presented numerical experiments.</jats:p>"
author:
- first_name: David
  full_name: Hipp, David
  last_name: Hipp
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: 'Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic
    boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>.
    2020;41(1):638-728. doi:<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>'
  apa: 'Hipp, D., &#38; Kovács, B. (2020). Finite element error analysis of wave equations
    with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical
    Analysis</i>, <i>41</i>(1), 638–728. <a href="https://doi.org/10.1093/imanum/drz073">https://doi.org/10.1093/imanum/drz073</a>'
  bibtex: '@article{Hipp_Kovács_2020, title={Finite element error analysis of wave
    equations with dynamic boundary conditions: <i>L</i>2 estimates}, volume={41},
    DOI={<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>},
    number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728}
    }'
  chicago: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave
    Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal
    of Numerical Analysis</i> 41, no. 1 (2020): 638–728. <a href="https://doi.org/10.1093/imanum/drz073">https://doi.org/10.1093/imanum/drz073</a>.'
  ieee: 'D. Hipp and B. Kovács, “Finite element error analysis of wave equations with
    dynamic boundary conditions: <i>L</i>2 estimates,” <i>IMA Journal of Numerical
    Analysis</i>, vol. 41, no. 1, pp. 638–728, 2020, doi: <a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>.'
  mla: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations
    with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical
    Analysis</i>, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728,
    doi:<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>.'
  short: D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728.
date_created: 2023-07-10T11:42:31Z
date_updated: 2024-04-03T09:20:44Z
department:
- _id: '841'
doi: 10.1093/imanum/drz073
intvolume: '        41'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 638-728
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: 'Finite element error analysis of wave equations with dynamic boundary conditions:
  <i>L</i>2 estimates'
type: journal_article
user_id: '100441'
volume: 41
year: '2020'
...