---
_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: '45959'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  last_name: Kovács
- first_name: Buyang
  full_name: Li, Buyang
  last_name: Li
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for
    Willmore flow of closed surfaces. <i>Numerische Mathematik</i>. 2021;149(3):595-643.
    doi:<a href="https://doi.org/10.1007/s00211-021-01238-z">10.1007/s00211-021-01238-z</a>
  apa: Kovács, B., Li, B., &#38; Lubich, C. (2021). A convergent evolving finite element
    algorithm for Willmore flow of closed surfaces. <i>Numerische Mathematik</i>,
    <i>149</i>(3), 595–643. <a href="https://doi.org/10.1007/s00211-021-01238-z">https://doi.org/10.1007/s00211-021-01238-z</a>
  bibtex: '@article{Kovács_Li_Lubich_2021, title={A convergent evolving finite element
    algorithm for Willmore flow of closed surfaces}, volume={149}, DOI={<a href="https://doi.org/10.1007/s00211-021-01238-z">10.1007/s00211-021-01238-z</a>},
    number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2021},
    pages={595–643} }'
  chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving
    Finite Element Algorithm for Willmore Flow of Closed Surfaces.” <i>Numerische
    Mathematik</i> 149, no. 3 (2021): 595–643. <a href="https://doi.org/10.1007/s00211-021-01238-z">https://doi.org/10.1007/s00211-021-01238-z</a>.'
  ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm
    for Willmore flow of closed surfaces,” <i>Numerische Mathematik</i>, vol. 149,
    no. 3, pp. 595–643, 2021, doi: <a href="https://doi.org/10.1007/s00211-021-01238-z">10.1007/s00211-021-01238-z</a>.'
  mla: Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for
    Willmore Flow of Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 149, no.
    3, Springer Science and Business Media LLC, 2021, pp. 595–643, doi:<a href="https://doi.org/10.1007/s00211-021-01238-z">10.1007/s00211-021-01238-z</a>.
  short: B. Kovács, B. Li, C. Lubich, Numerische Mathematik 149 (2021) 595–643.
date_created: 2023-07-10T11:43:59Z
date_updated: 2024-04-03T09:19:20Z
department:
- _id: '841'
doi: 10.1007/s00211-021-01238-z
intvolume: '       149'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 595-643
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A convergent evolving finite element algorithm for Willmore flow of closed
  surfaces
type: journal_article
user_id: '100441'
volume: 149
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: '45955'
author:
- first_name: Georgios
  full_name: Akrivis, Georgios
  last_name: Akrivis
- 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
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full
    discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>.
    2020;90(329):995-1038. doi:<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>
  apa: Akrivis, G., Feischl, M., Kovács, B., &#38; Lubich, C. (2020). Higher-order
    linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation.
    <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. <a href="https://doi.org/10.1090/mcom/3597">https://doi.org/10.1090/mcom/3597</a>
  bibtex: '@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly
    implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90},
    DOI={<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>}, number={329},
    journal={Mathematics of Computation}, publisher={American Mathematical Society
    (AMS)}, author={Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and
    Lubich, Christian}, year={2020}, pages={995–1038} }'
  chicago: 'Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich.
    “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert
    Equation.” <i>Mathematics of Computation</i> 90, no. 329 (2020): 995–1038. <a
    href="https://doi.org/10.1090/mcom/3597">https://doi.org/10.1090/mcom/3597</a>.'
  ieee: 'G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly
    implicit full discretization of the Landau–Lifshitz–Gilbert equation,” <i>Mathematics
    of Computation</i>, vol. 90, no. 329, pp. 995–1038, 2020, doi: <a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>.'
  mla: Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization
    of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i>, vol.
    90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>.
  short: G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation
    90 (2020) 995–1038.
date_created: 2023-07-10T11:42:57Z
date_updated: 2024-04-03T09:20:36Z
department:
- _id: '841'
doi: 10.1090/mcom/3597
intvolume: '        90'
issue: '329'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 995-1038
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert
  equation
type: journal_article
user_id: '100441'
volume: 90
year: '2020'
...
---
_id: '45952'
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
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Kovács B, Li B, Lubich C. A convergent algorithm for forced mean curvature
    flow driven by diffusion on the surface. <i>Interfaces and Free Boundaries</i>.
    2020;22(4):443-464. doi:<a href="https://doi.org/10.4171/ifb/446">10.4171/ifb/446</a>
  apa: Kovács, B., Li, B., &#38; Lubich, C. (2020). A convergent algorithm for forced
    mean curvature flow driven by diffusion on the surface. <i>Interfaces and Free
    Boundaries</i>, <i>22</i>(4), 443–464. <a href="https://doi.org/10.4171/ifb/446">https://doi.org/10.4171/ifb/446</a>
  bibtex: '@article{Kovács_Li_Lubich_2020, title={A convergent algorithm for forced
    mean curvature flow driven by diffusion on the surface}, volume={22}, DOI={<a
    href="https://doi.org/10.4171/ifb/446">10.4171/ifb/446</a>}, number={4}, journal={Interfaces
    and Free Boundaries}, publisher={European Mathematical Society - EMS - Publishing
    House GmbH}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2020},
    pages={443–464} }'
  chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Algorithm
    for Forced Mean Curvature Flow Driven by Diffusion on the Surface.” <i>Interfaces
    and Free Boundaries</i> 22, no. 4 (2020): 443–64. <a href="https://doi.org/10.4171/ifb/446">https://doi.org/10.4171/ifb/446</a>.'
  ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent algorithm for forced mean
    curvature flow driven by diffusion on the surface,” <i>Interfaces and Free Boundaries</i>,
    vol. 22, no. 4, pp. 443–464, 2020, doi: <a href="https://doi.org/10.4171/ifb/446">10.4171/ifb/446</a>.'
  mla: Kovács, Balázs, et al. “A Convergent Algorithm for Forced Mean Curvature Flow
    Driven by Diffusion on the Surface.” <i>Interfaces and Free Boundaries</i>, vol.
    22, no. 4, European Mathematical Society - EMS - Publishing House GmbH, 2020,
    pp. 443–64, doi:<a href="https://doi.org/10.4171/ifb/446">10.4171/ifb/446</a>.
  short: B. Kovács, B. Li, C. Lubich, Interfaces and Free Boundaries 22 (2020) 443–464.
date_created: 2023-07-10T11:42:14Z
date_updated: 2024-04-03T09:21:02Z
department:
- _id: '841'
doi: 10.4171/ifb/446
intvolume: '        22'
issue: '4'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 443-464
publication: Interfaces and Free Boundaries
publication_identifier:
  issn:
  - 1463-9963
publication_status: published
publisher: European Mathematical Society - EMS - Publishing House GmbH
status: public
title: A convergent algorithm for forced mean curvature flow driven by diffusion on
  the surface
type: journal_article
user_id: '100441'
volume: 22
year: '2020'
...
---
_id: '45948'
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
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for
    mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>. 2019;143(4):797-853.
    doi:<a href="https://doi.org/10.1007/s00211-019-01074-2">10.1007/s00211-019-01074-2</a>
  apa: Kovács, B., Li, B., &#38; Lubich, C. (2019). A convergent evolving finite element
    algorithm for mean curvature flow of closed surfaces. <i>Numerische Mathematik</i>,
    <i>143</i>(4), 797–853. <a href="https://doi.org/10.1007/s00211-019-01074-2">https://doi.org/10.1007/s00211-019-01074-2</a>
  bibtex: '@article{Kovács_Li_Lubich_2019, title={A convergent evolving finite element
    algorithm for mean curvature flow of closed surfaces}, volume={143}, DOI={<a href="https://doi.org/10.1007/s00211-019-01074-2">10.1007/s00211-019-01074-2</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2019},
    pages={797–853} }'
  chicago: 'Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving
    Finite Element Algorithm for Mean Curvature Flow of Closed Surfaces.” <i>Numerische
    Mathematik</i> 143, no. 4 (2019): 797–853. <a href="https://doi.org/10.1007/s00211-019-01074-2">https://doi.org/10.1007/s00211-019-01074-2</a>.'
  ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm
    for mean curvature flow of closed surfaces,” <i>Numerische Mathematik</i>, vol.
    143, no. 4, pp. 797–853, 2019, doi: <a href="https://doi.org/10.1007/s00211-019-01074-2">10.1007/s00211-019-01074-2</a>.'
  mla: Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for
    Mean Curvature Flow of Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 143,
    no. 4, Springer Science and Business Media LLC, 2019, pp. 797–853, doi:<a href="https://doi.org/10.1007/s00211-019-01074-2">10.1007/s00211-019-01074-2</a>.
  short: B. Kovács, B. Li, C. Lubich, Numerische Mathematik 143 (2019) 797–853.
date_created: 2023-07-10T11:40:56Z
date_updated: 2024-04-03T09:21:40Z
department:
- _id: '841'
doi: 10.1007/s00211-019-01074-2
intvolume: '       143'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 797-853
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A convergent evolving finite element algorithm for mean curvature flow of closed
  surfaces
type: journal_article
user_id: '100441'
volume: 143
year: '2019'
...
---
_id: '45974'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Kovács B. <i>Numerical Analysis of Partial Differential Equations on and of
    Evolving Surfaces</i>.; 2018.
  apa: Kovács, B. (2018). <i>Numerical analysis of partial differential equations
    on and of evolving surfaces</i>.
  bibtex: '@book{Kovács_2018, place={Tübingen, Germany}, title={Numerical analysis
    of partial differential equations on and of evolving surfaces}, author={Kovács,
    Balázs}, year={2018} }'
  chicago: Kovács, Balázs. <i>Numerical Analysis of Partial Differential Equations
    on and of Evolving Surfaces</i>. Tübingen, Germany, 2018.
  ieee: B. Kovács, <i>Numerical analysis of partial differential equations on and
    of evolving surfaces</i>. Tübingen, Germany, 2018.
  mla: Kovács, Balázs. <i>Numerical Analysis of Partial Differential Equations on
    and of Evolving Surfaces</i>. 2018.
  short: B. Kovács, Numerical Analysis of Partial Differential Equations on and of
    Evolving Surfaces, Tübingen, Germany, 2018.
date_created: 2023-07-10T12:37:48Z
date_updated: 2024-04-03T09:14:36Z
department:
- _id: '841'
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://na.uni-tuebingen.de/~kovacs/BKovacs_habilitation.pdf
oa: '1'
place: Tübingen, Germany
publication_status: published
status: public
supervisor:
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
title: Numerical analysis of partial differential equations on and of evolving surfaces
type: habilitation
user_id: '100441'
year: '2018'
...
---
_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: '45947'
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. Linearly implicit full discretization of surface evolution.
    <i>Numerische Mathematik</i>. 2018;140(1):121-152. doi:<a href="https://doi.org/10.1007/s00211-018-0962-6">10.1007/s00211-018-0962-6</a>
  apa: Kovács, B., &#38; Lubich, C. (2018). Linearly implicit full discretization
    of surface evolution. <i>Numerische Mathematik</i>, <i>140</i>(1), 121–152. <a
    href="https://doi.org/10.1007/s00211-018-0962-6">https://doi.org/10.1007/s00211-018-0962-6</a>
  bibtex: '@article{Kovács_Lubich_2018, title={Linearly implicit full discretization
    of surface evolution}, volume={140}, DOI={<a href="https://doi.org/10.1007/s00211-018-0962-6">10.1007/s00211-018-0962-6</a>},
    number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Lubich, Christian}, year={2018}, pages={121–152}
    }'
  chicago: 'Kovács, Balázs, and Christian Lubich. “Linearly Implicit Full Discretization
    of Surface Evolution.” <i>Numerische Mathematik</i> 140, no. 1 (2018): 121–52.
    <a href="https://doi.org/10.1007/s00211-018-0962-6">https://doi.org/10.1007/s00211-018-0962-6</a>.'
  ieee: 'B. Kovács and C. Lubich, “Linearly implicit full discretization of surface
    evolution,” <i>Numerische Mathematik</i>, vol. 140, no. 1, pp. 121–152, 2018,
    doi: <a href="https://doi.org/10.1007/s00211-018-0962-6">10.1007/s00211-018-0962-6</a>.'
  mla: Kovács, Balázs, and Christian Lubich. “Linearly Implicit Full Discretization
    of Surface Evolution.” <i>Numerische Mathematik</i>, vol. 140, no. 1, Springer
    Science and Business Media LLC, 2018, pp. 121–52, doi:<a href="https://doi.org/10.1007/s00211-018-0962-6">10.1007/s00211-018-0962-6</a>.
  short: B. Kovács, C. Lubich, Numerische Mathematik 140 (2018) 121–152.
date_created: 2023-07-10T11:40:40Z
date_updated: 2024-04-03T09:21:48Z
department:
- _id: '841'
doi: 10.1007/s00211-018-0962-6
intvolume: '       140'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 121-152
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Linearly implicit full discretization of surface evolution
type: journal_article
user_id: '100441'
volume: 140
year: '2018'
...
---
_id: '45951'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Kovács B. Computing arbitrary Lagrangian Eulerian maps for evolving surfaces.
    <i>Numerical Methods for Partial Differential Equations</i>. 2018;35(3):1093-1112.
    doi:<a href="https://doi.org/10.1002/num.22340">10.1002/num.22340</a>
  apa: Kovács, B. (2018). Computing arbitrary Lagrangian Eulerian maps for evolving
    surfaces. <i>Numerical Methods for Partial Differential Equations</i>, <i>35</i>(3),
    1093–1112. <a href="https://doi.org/10.1002/num.22340">https://doi.org/10.1002/num.22340</a>
  bibtex: '@article{Kovács_2018, title={Computing arbitrary Lagrangian Eulerian maps
    for evolving surfaces}, volume={35}, DOI={<a href="https://doi.org/10.1002/num.22340">10.1002/num.22340</a>},
    number={3}, journal={Numerical Methods for Partial Differential Equations}, publisher={Wiley},
    author={Kovács, Balázs}, year={2018}, pages={1093–1112} }'
  chicago: 'Kovács, Balázs. “Computing Arbitrary Lagrangian Eulerian Maps for Evolving
    Surfaces.” <i>Numerical Methods for Partial Differential Equations</i> 35, no.
    3 (2018): 1093–1112. <a href="https://doi.org/10.1002/num.22340">https://doi.org/10.1002/num.22340</a>.'
  ieee: 'B. Kovács, “Computing arbitrary Lagrangian Eulerian maps for evolving surfaces,”
    <i>Numerical Methods for Partial Differential Equations</i>, vol. 35, no. 3, pp.
    1093–1112, 2018, doi: <a href="https://doi.org/10.1002/num.22340">10.1002/num.22340</a>.'
  mla: Kovács, Balázs. “Computing Arbitrary Lagrangian Eulerian Maps for Evolving
    Surfaces.” <i>Numerical Methods for Partial Differential Equations</i>, vol. 35,
    no. 3, Wiley, 2018, pp. 1093–112, doi:<a href="https://doi.org/10.1002/num.22340">10.1002/num.22340</a>.
  short: B. Kovács, Numerical Methods for Partial Differential Equations 35 (2018)
    1093–1112.
date_created: 2023-07-10T11:41:54Z
date_updated: 2024-04-03T09:21:13Z
department:
- _id: '841'
doi: 10.1002/num.22340
intvolume: '        35'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
- Analysis
language:
- iso: eng
page: 1093-1112
publication: Numerical Methods for Partial Differential Equations
publication_identifier:
  issn:
  - 0749-159X
  - 1098-2426
publication_status: published
publisher: Wiley
status: public
title: Computing arbitrary Lagrangian Eulerian maps for evolving surfaces
type: journal_article
user_id: '100441'
volume: 35
year: '2018'
...
---
_id: '45941'
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
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
- first_name: Christian A.
  full_name: Power Guerra, Christian A.
  last_name: Power Guerra
citation:
  ama: Kovács B, Li B, Lubich C, Power Guerra CA. Convergence of finite elements on
    an evolving surface driven by diffusion on the surface. <i>Numerische Mathematik</i>.
    2017;137(3):643-689. doi:<a href="https://doi.org/10.1007/s00211-017-0888-4">10.1007/s00211-017-0888-4</a>
  apa: Kovács, B., Li, B., Lubich, C., &#38; Power Guerra, C. A. (2017). Convergence
    of finite elements on an evolving surface driven by diffusion on the surface.
    <i>Numerische Mathematik</i>, <i>137</i>(3), 643–689. <a href="https://doi.org/10.1007/s00211-017-0888-4">https://doi.org/10.1007/s00211-017-0888-4</a>
  bibtex: '@article{Kovács_Li_Lubich_Power Guerra_2017, title={Convergence of finite
    elements on an evolving surface driven by diffusion on the surface}, volume={137},
    DOI={<a href="https://doi.org/10.1007/s00211-017-0888-4">10.1007/s00211-017-0888-4</a>},
    number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian and Power
    Guerra, Christian A.}, year={2017}, pages={643–689} }'
  chicago: 'Kovács, Balázs, Buyang Li, Christian Lubich, and Christian A. Power Guerra.
    “Convergence of Finite Elements on an Evolving Surface Driven by Diffusion on
    the Surface.” <i>Numerische Mathematik</i> 137, no. 3 (2017): 643–89. <a href="https://doi.org/10.1007/s00211-017-0888-4">https://doi.org/10.1007/s00211-017-0888-4</a>.'
  ieee: 'B. Kovács, B. Li, C. Lubich, and C. A. Power Guerra, “Convergence of finite
    elements on an evolving surface driven by diffusion on the surface,” <i>Numerische
    Mathematik</i>, vol. 137, no. 3, pp. 643–689, 2017, doi: <a href="https://doi.org/10.1007/s00211-017-0888-4">10.1007/s00211-017-0888-4</a>.'
  mla: Kovács, Balázs, et al. “Convergence of Finite Elements on an Evolving Surface
    Driven by Diffusion on the Surface.” <i>Numerische Mathematik</i>, vol. 137, no.
    3, Springer Science and Business Media LLC, 2017, pp. 643–89, doi:<a href="https://doi.org/10.1007/s00211-017-0888-4">10.1007/s00211-017-0888-4</a>.
  short: B. Kovács, B. Li, C. Lubich, C.A. Power Guerra, Numerische Mathematik 137
    (2017) 643–689.
date_created: 2023-07-10T11:38:48Z
date_updated: 2024-04-03T09:22:43Z
department:
- _id: '841'
doi: 10.1007/s00211-017-0888-4
intvolume: '       137'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 643-689
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Convergence of finite elements on an evolving surface driven by diffusion on
  the surface
type: journal_article
user_id: '100441'
volume: 137
year: '2017'
...
---
_id: '45942'
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. Stability and convergence of time discretizations of quasi-linear
    evolution equations of Kato type. <i>Numerische Mathematik</i>. 2017;138(2):365-388.
    doi:<a href="https://doi.org/10.1007/s00211-017-0909-3">10.1007/s00211-017-0909-3</a>
  apa: Kovács, B., &#38; Lubich, C. (2017). Stability and convergence of time discretizations
    of quasi-linear evolution equations of Kato type. <i>Numerische Mathematik</i>,
    <i>138</i>(2), 365–388. <a href="https://doi.org/10.1007/s00211-017-0909-3">https://doi.org/10.1007/s00211-017-0909-3</a>
  bibtex: '@article{Kovács_Lubich_2017, title={Stability and convergence of time discretizations
    of quasi-linear evolution equations of Kato type}, volume={138}, DOI={<a href="https://doi.org/10.1007/s00211-017-0909-3">10.1007/s00211-017-0909-3</a>},
    number={2}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Lubich, Christian}, year={2017}, pages={365–388}
    }'
  chicago: 'Kovács, Balázs, and Christian Lubich. “Stability and Convergence of Time
    Discretizations of Quasi-Linear Evolution Equations of Kato Type.” <i>Numerische
    Mathematik</i> 138, no. 2 (2017): 365–88. <a href="https://doi.org/10.1007/s00211-017-0909-3">https://doi.org/10.1007/s00211-017-0909-3</a>.'
  ieee: 'B. Kovács and C. Lubich, “Stability and convergence of time discretizations
    of quasi-linear evolution equations of Kato type,” <i>Numerische Mathematik</i>,
    vol. 138, no. 2, pp. 365–388, 2017, doi: <a href="https://doi.org/10.1007/s00211-017-0909-3">10.1007/s00211-017-0909-3</a>.'
  mla: Kovács, Balázs, and Christian Lubich. “Stability and Convergence of Time Discretizations
    of Quasi-Linear Evolution Equations of Kato Type.” <i>Numerische Mathematik</i>,
    vol. 138, no. 2, Springer Science and Business Media LLC, 2017, pp. 365–88, doi:<a
    href="https://doi.org/10.1007/s00211-017-0909-3">10.1007/s00211-017-0909-3</a>.
  short: B. Kovács, C. Lubich, Numerische Mathematik 138 (2017) 365–388.
date_created: 2023-07-10T11:39:05Z
date_updated: 2024-04-03T09:22:34Z
department:
- _id: '841'
doi: 10.1007/s00211-017-0909-3
intvolume: '       138'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 365-388
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 convergence of time discretizations of quasi-linear evolution
  equations of Kato type
type: journal_article
user_id: '100441'
volume: 138
year: '2017'
...
---
_id: '45940'
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. Stable and convergent fully discrete interior–exterior
    coupling of Maxwell’s equations. <i>Numerische Mathematik</i>. 2017;137(1):91-117.
    doi:<a href="https://doi.org/10.1007/s00211-017-0868-8">10.1007/s00211-017-0868-8</a>
  apa: Kovács, B., &#38; Lubich, C. (2017). Stable and convergent fully discrete interior–exterior
    coupling of Maxwell’s equations. <i>Numerische Mathematik</i>, <i>137</i>(1),
    91–117. <a href="https://doi.org/10.1007/s00211-017-0868-8">https://doi.org/10.1007/s00211-017-0868-8</a>
  bibtex: '@article{Kovács_Lubich_2017, title={Stable and convergent fully discrete
    interior–exterior coupling of Maxwell’s equations}, volume={137}, DOI={<a href="https://doi.org/10.1007/s00211-017-0868-8">10.1007/s00211-017-0868-8</a>},
    number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kovács, Balázs and Lubich, Christian}, year={2017}, pages={91–117}
    }'
  chicago: 'Kovács, Balázs, and Christian Lubich. “Stable and Convergent Fully Discrete
    Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>
    137, no. 1 (2017): 91–117. <a href="https://doi.org/10.1007/s00211-017-0868-8">https://doi.org/10.1007/s00211-017-0868-8</a>.'
  ieee: 'B. Kovács and C. Lubich, “Stable and convergent fully discrete interior–exterior
    coupling of Maxwell’s equations,” <i>Numerische Mathematik</i>, vol. 137, no.
    1, pp. 91–117, 2017, doi: <a href="https://doi.org/10.1007/s00211-017-0868-8">10.1007/s00211-017-0868-8</a>.'
  mla: Kovács, Balázs, and Christian Lubich. “Stable and Convergent Fully Discrete
    Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>,
    vol. 137, no. 1, Springer Science and Business Media LLC, 2017, pp. 91–117, doi:<a
    href="https://doi.org/10.1007/s00211-017-0868-8">10.1007/s00211-017-0868-8</a>.
  short: B. Kovács, C. Lubich, Numerische Mathematik 137 (2017) 91–117.
date_created: 2023-07-10T11:38:34Z
date_updated: 2024-04-03T09:22:51Z
department:
- _id: '841'
doi: 10.1007/s00211-017-0868-8
intvolume: '       137'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 91-117
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s
  equations
type: journal_article
user_id: '100441'
volume: 137
year: '2017'
...
---
_id: '45946'
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. Maximum norm stability and error estimates for the
    evolving surface finite element method. <i>Numerical Methods for Partial Differential
    Equations</i>. 2017;34(2):518-554. doi:<a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>
  apa: Kovács, B., &#38; Power Guerra, C. A. (2017). Maximum norm stability and error
    estimates for the evolving surface finite element method. <i>Numerical Methods
    for Partial Differential Equations</i>, <i>34</i>(2), 518–554. <a href="https://doi.org/10.1002/num.22212">https://doi.org/10.1002/num.22212</a>
  bibtex: '@article{Kovács_Power Guerra_2017, title={Maximum norm stability and error
    estimates for the evolving surface finite element method}, volume={34}, DOI={<a
    href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>}, number={2}, journal={Numerical
    Methods for Partial Differential Equations}, publisher={Wiley}, author={Kovács,
    Balázs and Power Guerra, Christian Andreas}, year={2017}, pages={518–554} }'
  chicago: 'Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability
    and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical
    Methods for Partial Differential Equations</i> 34, no. 2 (2017): 518–54. <a href="https://doi.org/10.1002/num.22212">https://doi.org/10.1002/num.22212</a>.'
  ieee: 'B. Kovács and C. A. Power Guerra, “Maximum norm stability and error estimates
    for the evolving surface finite element method,” <i>Numerical Methods for Partial
    Differential Equations</i>, vol. 34, no. 2, pp. 518–554, 2017, doi: <a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>.'
  mla: Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability
    and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical
    Methods for Partial Differential Equations</i>, vol. 34, no. 2, Wiley, 2017, pp.
    518–54, doi:<a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>.
  short: B. Kovács, C.A. Power Guerra, Numerical Methods for Partial Differential
    Equations 34 (2017) 518–554.
date_created: 2023-07-10T11:40:24Z
date_updated: 2024-04-03T09:22:00Z
department:
- _id: '841'
doi: 10.1002/num.22212
intvolume: '        34'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
- Analysis
language:
- iso: eng
page: 518-554
publication: Numerical Methods for Partial Differential Equations
publication_identifier:
  issn:
  - 0749-159X
publication_status: published
publisher: Wiley
status: public
title: Maximum norm stability and error estimates for the evolving surface finite
  element method
type: journal_article
user_id: '100441'
volume: 34
year: '2017'
...
---
_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: '45945'
author:
- first_name: Balázs
  full_name: Kovács, Balázs
  last_name: Kovács
- first_name: Christian Andreas
  full_name: Power Guerra, Christian Andreas
  last_name: Power Guerra
citation:
  ama: Kovács B, Power Guerra CA. Maximum norm stability and error estimates for the
    evolving surface finite element method. <i>Numerical Methods for Partial Differential
    Equations</i>. 2017;34(2):518-554. doi:<a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>
  apa: Kovács, B., &#38; Power Guerra, C. A. (2017). Maximum norm stability and error
    estimates for the evolving surface finite element method. <i>Numerical Methods
    for Partial Differential Equations</i>, <i>34</i>(2), 518–554. <a href="https://doi.org/10.1002/num.22212">https://doi.org/10.1002/num.22212</a>
  bibtex: '@article{Kovács_Power Guerra_2017, title={Maximum norm stability and error
    estimates for the evolving surface finite element method}, volume={34}, DOI={<a
    href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>}, number={2}, journal={Numerical
    Methods for Partial Differential Equations}, publisher={Wiley}, author={Kovács,
    Balázs and Power Guerra, Christian Andreas}, year={2017}, pages={518–554} }'
  chicago: 'Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability
    and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical
    Methods for Partial Differential Equations</i> 34, no. 2 (2017): 518–54. <a href="https://doi.org/10.1002/num.22212">https://doi.org/10.1002/num.22212</a>.'
  ieee: 'B. Kovács and C. A. Power Guerra, “Maximum norm stability and error estimates
    for the evolving surface finite element method,” <i>Numerical Methods for Partial
    Differential Equations</i>, vol. 34, no. 2, pp. 518–554, 2017, doi: <a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>.'
  mla: Kovács, Balázs, and Christian Andreas Power Guerra. “Maximum Norm Stability
    and Error Estimates for the Evolving Surface Finite Element Method.” <i>Numerical
    Methods for Partial Differential Equations</i>, vol. 34, no. 2, Wiley, 2017, pp.
    518–54, doi:<a href="https://doi.org/10.1002/num.22212">10.1002/num.22212</a>.
  short: B. Kovács, C.A. Power Guerra, Numerical Methods for Partial Differential
    Equations 34 (2017) 518–554.
date_created: 2023-07-10T11:40:00Z
date_updated: 2024-04-03T09:22:09Z
department:
- _id: '841'
doi: 10.1002/num.22212
intvolume: '        34'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
- Analysis
language:
- iso: eng
page: 518-554
publication: Numerical Methods for Partial Differential Equations
publication_identifier:
  issn:
  - 0749-159X
publication_status: published
publisher: Wiley
status: public
title: Maximum norm stability and error estimates for the evolving surface finite
  element method
type: journal_article
user_id: '100441'
volume: 34
year: '2017'
...