---
_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: '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: '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: '45954'
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
  last_name: Kovács
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: 2023-07-10T11:42:43Z
date_updated: 2024-04-03T09:14:14Z
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'
...
---
_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'
...
---
_id: '45950'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important
    qualitative property of second-order elliptic equations; therefore, its discrete
    analogues, the so-called discrete maximum principles (DMPs), have drawn much attention
    owing to their role in reinforcing the qualitative reliability of the given numerical
    scheme. In this paper DMPs are established for nonlinear finite element problems
    on surfaces with boundary, corresponding to the classical pointwise maximum principles
    on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum
    Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>
author:
- first_name: János
  full_name: Karátson, János
  last_name: Karátson
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Sergey
  full_name: Korotov, Sergey
  last_name: Korotov
citation:
  ama: Karátson J, Kovács B, Korotov S. Discrete maximum principles for nonlinear
    elliptic finite element problems on surfaces with boundary. <i>IMA Journal of
    Numerical Analysis</i>. 2018;40(2):1241-1265. doi:<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>
  apa: Karátson, J., Kovács, B., &#38; Korotov, S. (2018). Discrete maximum principles
    for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA
    Journal of Numerical Analysis</i>, <i>40</i>(2), 1241–1265. <a href="https://doi.org/10.1093/imanum/dry086">https://doi.org/10.1093/imanum/dry086</a>
  bibtex: '@article{Karátson_Kovács_Korotov_2018, title={Discrete maximum principles
    for nonlinear elliptic finite element problems on surfaces with boundary}, volume={40},
    DOI={<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>},
    number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Karátson, János and Kovács, Balázs and Korotov, Sergey},
    year={2018}, pages={1241–1265} }'
  chicago: 'Karátson, János, Balázs Kovács, and Sergey Korotov. “Discrete Maximum
    Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.”
    <i>IMA Journal of Numerical Analysis</i> 40, no. 2 (2018): 1241–65. <a href="https://doi.org/10.1093/imanum/dry086">https://doi.org/10.1093/imanum/dry086</a>.'
  ieee: 'J. Karátson, B. Kovács, and S. Korotov, “Discrete maximum principles for
    nonlinear elliptic finite element problems on surfaces with boundary,” <i>IMA
    Journal of Numerical Analysis</i>, vol. 40, no. 2, pp. 1241–1265, 2018, doi: <a
    href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>.'
  mla: Karátson, János, et al. “Discrete Maximum Principles for Nonlinear Elliptic
    Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical
    Analysis</i>, vol. 40, no. 2, Oxford University Press (OUP), 2018, pp. 1241–65,
    doi:<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>.
  short: J. Karátson, B. Kovács, S. Korotov, IMA Journal of Numerical Analysis 40
    (2018) 1241–1265.
date_created: 2023-07-10T11:41:27Z
date_updated: 2024-04-03T09:21:21Z
department:
- _id: '841'
doi: 10.1093/imanum/dry086
intvolume: '        40'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 1241-1265
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Discrete maximum principles for nonlinear elliptic finite element problems
  on surfaces with boundary
type: journal_article
user_id: '100441'
volume: 40
year: '2018'
...
---
_id: '45949'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The maximum principle forms an important
    qualitative property of second-order elliptic equations; therefore, its discrete
    analogues, the so-called discrete maximum principles (DMPs), have drawn much attention
    owing to their role in reinforcing the qualitative reliability of the given numerical
    scheme. In this paper DMPs are established for nonlinear finite element problems
    on surfaces with boundary, corresponding to the classical pointwise maximum principles
    on Riemannian manifolds in the spirit of Pucci &amp; Serrin (2007, The Maximum
    Principle. Springer). Various real-life examples illustrate the scope of the results.</jats:p>
author:
- first_name: János
  full_name: Karátson, János
  last_name: Karátson
- first_name: Balázs
  full_name: Kovács, Balázs
  last_name: Kovács
- first_name: Sergey
  full_name: Korotov, Sergey
  last_name: Korotov
citation:
  ama: Karátson J, Kovács B, Korotov S. Discrete maximum principles for nonlinear
    elliptic finite element problems on surfaces with boundary. <i>IMA Journal of
    Numerical Analysis</i>. 2018;40(2):1241-1265. doi:<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>
  apa: Karátson, J., Kovács, B., &#38; Korotov, S. (2018). Discrete maximum principles
    for nonlinear elliptic finite element problems on surfaces with boundary. <i>IMA
    Journal of Numerical Analysis</i>, <i>40</i>(2), 1241–1265. <a href="https://doi.org/10.1093/imanum/dry086">https://doi.org/10.1093/imanum/dry086</a>
  bibtex: '@article{Karátson_Kovács_Korotov_2018, title={Discrete maximum principles
    for nonlinear elliptic finite element problems on surfaces with boundary}, volume={40},
    DOI={<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>},
    number={2}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Karátson, János and Kovács, Balázs and Korotov, Sergey},
    year={2018}, pages={1241–1265} }'
  chicago: 'Karátson, János, Balázs Kovács, and Sergey Korotov. “Discrete Maximum
    Principles for Nonlinear Elliptic Finite Element Problems on Surfaces with Boundary.”
    <i>IMA Journal of Numerical Analysis</i> 40, no. 2 (2018): 1241–65. <a href="https://doi.org/10.1093/imanum/dry086">https://doi.org/10.1093/imanum/dry086</a>.'
  ieee: 'J. Karátson, B. Kovács, and S. Korotov, “Discrete maximum principles for
    nonlinear elliptic finite element problems on surfaces with boundary,” <i>IMA
    Journal of Numerical Analysis</i>, vol. 40, no. 2, pp. 1241–1265, 2018, doi: <a
    href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>.'
  mla: Karátson, János, et al. “Discrete Maximum Principles for Nonlinear Elliptic
    Finite Element Problems on Surfaces with Boundary.” <i>IMA Journal of Numerical
    Analysis</i>, vol. 40, no. 2, Oxford University Press (OUP), 2018, pp. 1241–65,
    doi:<a href="https://doi.org/10.1093/imanum/dry086">10.1093/imanum/dry086</a>.
  short: J. Karátson, B. Kovács, S. Korotov, IMA Journal of Numerical Analysis 40
    (2018) 1241–1265.
date_created: 2023-07-10T11:41:19Z
date_updated: 2024-04-03T09:21:29Z
department:
- _id: '841'
doi: 10.1093/imanum/dry086
intvolume: '        40'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 1241-1265
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Discrete maximum principles for nonlinear elliptic finite element problems
  on surfaces with boundary
type: journal_article
user_id: '100441'
volume: 40
year: '2018'
...
---
_id: '45943'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Kovács B. High-order evolving surface finite element method for parabolic problems
    on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>. 2017;38(1):430-459.
    doi:<a href="https://doi.org/10.1093/imanum/drx013">10.1093/imanum/drx013</a>
  apa: Kovács, B. (2017). High-order evolving surface finite element method for parabolic
    problems on evolving surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>38</i>(1),
    430–459. <a href="https://doi.org/10.1093/imanum/drx013">https://doi.org/10.1093/imanum/drx013</a>
  bibtex: '@article{Kovács_2017, title={High-order evolving surface finite element
    method for parabolic problems on evolving surfaces}, volume={38}, DOI={<a href="https://doi.org/10.1093/imanum/drx013">10.1093/imanum/drx013</a>},
    number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Kovács, Balázs}, year={2017}, pages={430–459} }'
  chicago: 'Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for
    Parabolic Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>
    38, no. 1 (2017): 430–59. <a href="https://doi.org/10.1093/imanum/drx013">https://doi.org/10.1093/imanum/drx013</a>.'
  ieee: 'B. Kovács, “High-order evolving surface finite element method for parabolic
    problems on evolving surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol.
    38, no. 1, pp. 430–459, 2017, doi: <a href="https://doi.org/10.1093/imanum/drx013">10.1093/imanum/drx013</a>.'
  mla: Kovács, Balázs. “High-Order Evolving Surface Finite Element Method for Parabolic
    Problems on Evolving Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol.
    38, no. 1, Oxford University Press (OUP), 2017, pp. 430–59, doi:<a href="https://doi.org/10.1093/imanum/drx013">10.1093/imanum/drx013</a>.
  short: B. Kovács, IMA Journal of Numerical Analysis 38 (2017) 430–459.
date_created: 2023-07-10T11:39:23Z
date_updated: 2024-04-03T09:22:26Z
department:
- _id: '841'
doi: 10.1093/imanum/drx013
intvolume: '        38'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 430-459
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: High-order evolving surface finite element method for parabolic problems on
  evolving surfaces
type: journal_article
user_id: '100441'
volume: 38
year: '2017'
...
---
_id: '45944'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian Andreas
  full_name: Power Guerra, Christian Andreas
  last_name: Power Guerra
citation:
  ama: Kovács B, Power Guerra CA. Higher order time discretizations with ALE finite
    elements for parabolic problems on evolving surfaces. <i>IMA Journal of Numerical
    Analysis</i>. 2016;38(1):460-494. doi:<a href="https://doi.org/10.1093/imanum/drw074">10.1093/imanum/drw074</a>
  apa: Kovács, B., &#38; Power Guerra, C. A. (2016). Higher order time discretizations
    with ALE finite elements for parabolic problems on evolving surfaces. <i>IMA Journal
    of Numerical Analysis</i>, <i>38</i>(1), 460–494. <a href="https://doi.org/10.1093/imanum/drw074">https://doi.org/10.1093/imanum/drw074</a>
  bibtex: '@article{Kovács_Power Guerra_2016, title={Higher order time discretizations
    with ALE finite elements for parabolic problems on evolving surfaces}, volume={38},
    DOI={<a href="https://doi.org/10.1093/imanum/drw074">10.1093/imanum/drw074</a>},
    number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Kovács, Balázs and Power Guerra, Christian Andreas}, year={2016},
    pages={460–494} }'
  chicago: 'Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time
    Discretizations with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.”
    <i>IMA Journal of Numerical Analysis</i> 38, no. 1 (2016): 460–94. <a href="https://doi.org/10.1093/imanum/drw074">https://doi.org/10.1093/imanum/drw074</a>.'
  ieee: 'B. Kovács and C. A. Power Guerra, “Higher order time discretizations with
    ALE finite elements for parabolic problems on evolving surfaces,” <i>IMA Journal
    of Numerical Analysis</i>, vol. 38, no. 1, pp. 460–494, 2016, doi: <a href="https://doi.org/10.1093/imanum/drw074">10.1093/imanum/drw074</a>.'
  mla: Kovács, Balázs, and Christian Andreas Power Guerra. “Higher Order Time Discretizations
    with ALE Finite Elements for Parabolic Problems on Evolving Surfaces.” <i>IMA
    Journal of Numerical Analysis</i>, vol. 38, no. 1, Oxford University Press (OUP),
    2016, pp. 460–94, doi:<a href="https://doi.org/10.1093/imanum/drw074">10.1093/imanum/drw074</a>.
  short: B. Kovács, C.A. Power Guerra, IMA Journal of Numerical Analysis 38 (2016)
    460–494.
date_created: 2023-07-10T11:39:39Z
date_updated: 2024-04-03T09:22:19Z
department:
- _id: '841'
doi: 10.1093/imanum/drw074
intvolume: '        38'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 460-494
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Higher order time discretizations with ALE finite elements for parabolic problems
  on evolving surfaces
type: journal_article
user_id: '100441'
volume: 38
year: '2016'
...
---
_id: '45937'
author:
- 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: Kovács B, Lubich C. Numerical analysis of parabolic problems with dynamic boundary
    conditions. <i>IMA Journal of Numerical Analysis</i>. 2016;37(1):1-39. doi:<a
    href="https://doi.org/10.1093/imanum/drw015">10.1093/imanum/drw015</a>
  apa: Kovács, B., &#38; Lubich, C. (2016). Numerical analysis of parabolic problems
    with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>37</i>(1),
    1–39. <a href="https://doi.org/10.1093/imanum/drw015">https://doi.org/10.1093/imanum/drw015</a>
  bibtex: '@article{Kovács_Lubich_2016, title={Numerical analysis of parabolic problems
    with dynamic boundary conditions}, volume={37}, DOI={<a href="https://doi.org/10.1093/imanum/drw015">10.1093/imanum/drw015</a>},
    number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Kovács, Balázs and Lubich, Christian}, year={2016}, pages={1–39}
    }'
  chicago: 'Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic
    Problems with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>
    37, no. 1 (2016): 1–39. <a href="https://doi.org/10.1093/imanum/drw015">https://doi.org/10.1093/imanum/drw015</a>.'
  ieee: 'B. Kovács and C. Lubich, “Numerical analysis of parabolic problems with dynamic
    boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 37, no. 1,
    pp. 1–39, 2016, doi: <a href="https://doi.org/10.1093/imanum/drw015">10.1093/imanum/drw015</a>.'
  mla: Kovács, Balázs, and Christian Lubich. “Numerical Analysis of Parabolic Problems
    with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol.
    37, no. 1, Oxford University Press (OUP), 2016, pp. 1–39, doi:<a href="https://doi.org/10.1093/imanum/drw015">10.1093/imanum/drw015</a>.
  short: B. Kovács, C. Lubich, IMA Journal of Numerical Analysis 37 (2016) 1–39.
date_created: 2023-07-10T11:35:53Z
date_updated: 2024-04-03T09:23:16Z
department:
- _id: '841'
doi: 10.1093/imanum/drw015
intvolume: '        37'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 1-39
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Numerical analysis of parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 37
year: '2016'
...
---
_id: '16556'
author:
- first_name: M.
  full_name: Dellnitz, M.
  last_name: Dellnitz
citation:
  ama: Dellnitz M. Finding zeros by multilevel subdivision techniques. <i>IMA Journal
    of Numerical Analysis</i>. 2002:167-185. doi:<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>
  apa: Dellnitz, M. (2002). Finding zeros by multilevel subdivision techniques. <i>IMA
    Journal of Numerical Analysis</i>, 167–185. <a href="https://doi.org/10.1093/imanum/22.2.167">https://doi.org/10.1093/imanum/22.2.167</a>
  bibtex: '@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision
    techniques}, DOI={<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>},
    journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002},
    pages={167–185} }'
  chicago: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA
    Journal of Numerical Analysis</i>, 2002, 167–85. <a href="https://doi.org/10.1093/imanum/22.2.167">https://doi.org/10.1093/imanum/22.2.167</a>.
  ieee: M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” <i>IMA
    Journal of Numerical Analysis</i>, pp. 167–185, 2002.
  mla: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” <i>IMA Journal
    of Numerical Analysis</i>, 2002, pp. 167–85, doi:<a href="https://doi.org/10.1093/imanum/22.2.167">10.1093/imanum/22.2.167</a>.
  short: M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185.
date_created: 2020-04-15T09:12:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1093/imanum/22.2.167
language:
- iso: eng
page: 167-185
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
status: public
title: Finding zeros by multilevel subdivision techniques
type: journal_article
user_id: '15701'
year: '2002'
...