---
_id: '45969'
abstract:
- lang: eng
  text: '<jats:title>Abstract</jats:title><jats:p>An evolving surface finite element
    discretisation is analysed for the evolution of a closed two-dimensional surface
    governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion
    process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms
    are proposed, both based on a system coupling the diffusion equation to evolution
    equations for geometric quantities in the velocity law for the surface. One of
    the numerical methods is proved to be convergent in the<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$</jats:tex-math><mml:math
    xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math></jats:alternatives></jats:inline-formula>norm
    with optimal-order for finite elements of degree at least two. We present numerical
    experiments illustrating the convergence behaviour and demonstrating the qualitative
    properties of the flow: preservation of mean convexity, loss of convexity, weak
    maximum principles, and the occurrence of self-intersections.</jats:p>'
author:
- first_name: Charles M.
  full_name: Elliott, Charles M.
  last_name: Elliott
- first_name: Harald
  full_name: Garcke, Harald
  last_name: Garcke
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Elliott CM, Garcke H, Kovács B. Numerical analysis for the interaction of mean
    curvature flow and diffusion on closed surfaces. <i>Numerische Mathematik</i>.
    2022;151(4):873-925. doi:<a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>
  apa: Elliott, C. M., Garcke, H., &#38; Kovács, B. (2022). Numerical analysis for
    the interaction of mean curvature flow and diffusion on closed surfaces. <i>Numerische
    Mathematik</i>, <i>151</i>(4), 873–925. <a href="https://doi.org/10.1007/s00211-022-01301-3">https://doi.org/10.1007/s00211-022-01301-3</a>
  bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
    interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
    DOI={<a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Elliott, Charles M. and Garcke, Harald and Kovács, Balázs},
    year={2022}, pages={873–925} }'
  chicago: 'Elliott, Charles M., Harald Garcke, and Balázs Kovács. “Numerical Analysis
    for the Interaction of Mean Curvature Flow and Diffusion on Closed Surfaces.”
    <i>Numerische Mathematik</i> 151, no. 4 (2022): 873–925. <a href="https://doi.org/10.1007/s00211-022-01301-3">https://doi.org/10.1007/s00211-022-01301-3</a>.'
  ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
    of mean curvature flow and diffusion on closed surfaces,” <i>Numerische Mathematik</i>,
    vol. 151, no. 4, pp. 873–925, 2022, doi: <a href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>.'
  mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
    Curvature Flow and Diffusion on Closed Surfaces.” <i>Numerische Mathematik</i>,
    vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:<a
    href="https://doi.org/10.1007/s00211-022-01301-3">10.1007/s00211-022-01301-3</a>.
  short: C.M. Elliott, H. Garcke, B. Kovács, Numerische Mathematik 151 (2022) 873–925.
date_created: 2023-07-10T11:47:11Z
date_updated: 2024-04-03T09:15:44Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01301-3
intvolume: '       151'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 873-925
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Numerical analysis for the interaction of mean curvature flow and diffusion
  on closed surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45963'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>The scattering of electromagnetic
    waves from obstacles with wave-material interaction in thin layers on the surface
    is described by generalized impedance boundary conditions, which provide effective
    approximate models. In particular, this includes a thin coating around a perfect
    conductor and the skin effect of a highly conducting material. The approach taken
    in this work is to derive, analyse and discretize a system of time-dependent boundary
    integral equations that determines the tangential traces of the scattered electric
    and magnetic fields. In a familiar second step, the fields are evaluated in the
    exterior domain by a representation formula, which uses the time-dependent potential
    operators of Maxwell’s equations. The time-dependent boundary integral equation
    is discretized with Runge–Kutta based convolution quadrature in time and Raviart–Thomas
    boundary elements in space. Using the frequency-explicit bounds from the well-posedness
    analysis given here together with known approximation properties of the numerical
    methods, the full discretization is proved to be stable and convergent, with explicitly
    given rates in the case of sufficient regularity. Taking the same Runge–Kutta
    based convolution quadrature for discretizing the time-dependent representation
    formulas, the optimal order of convergence is obtained away from the scattering
    boundary, whereas an order reduction occurs close to the boundary. The theoretical
    results are illustrated by numerical experiments.</jats:p>
author:
- first_name: Jörg
  full_name: Nick, Jörg
  last_name: Nick
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Nick J, Kovács B, Lubich C. Time-dependent electromagnetic scattering from
    thin layers. <i>Numerische Mathematik</i>. 2022;150(4):1123-1164. doi:<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>
  apa: Nick, J., Kovács, B., &#38; Lubich, C. (2022). Time-dependent electromagnetic
    scattering from thin layers. <i>Numerische Mathematik</i>, <i>150</i>(4), 1123–1164.
    <a href="https://doi.org/10.1007/s00211-022-01277-0">https://doi.org/10.1007/s00211-022-01277-0</a>
  bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
    scattering from thin layers}, volume={150}, DOI={<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>},
    number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2022},
    pages={1123–1164} }'
  chicago: 'Nick, Jörg, Balázs Kovács, and Christian Lubich. “Time-Dependent Electromagnetic
    Scattering from Thin Layers.” <i>Numerische Mathematik</i> 150, no. 4 (2022):
    1123–64. <a href="https://doi.org/10.1007/s00211-022-01277-0">https://doi.org/10.1007/s00211-022-01277-0</a>.'
  ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
    from thin layers,” <i>Numerische Mathematik</i>, vol. 150, no. 4, pp. 1123–1164,
    2022, doi: <a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>.'
  mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
    <i>Numerische Mathematik</i>, vol. 150, no. 4, Springer Science and Business Media
    LLC, 2022, pp. 1123–64, doi:<a href="https://doi.org/10.1007/s00211-022-01277-0">10.1007/s00211-022-01277-0</a>.
  short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: '       150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>In this paper, we consider a non-linear
    fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with
    prescribed velocity, where the non-linear terms are only assumed to have locally
    Lipschitz derivatives. High-order evolving surface finite elements are used to
    discretise the weak equation system in space, and a modified matrix–vector formulation
    for the semi-discrete problem is derived. The anti-symmetric structure of the
    equation system is preserved by the spatial discretisation. A new stability proof,
    based on this structure, combined with consistency bounds proves optimal-order
    and uniform-in-time error estimates. The paper is concluded by a variety of numerical
    experiments.</jats:p>
author:
- first_name: Cedric Aaron
  full_name: Beschle, Cedric Aaron
  last_name: Beschle
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
citation:
  ama: Beschle CA, Kovács B. Stability and error estimates for non-linear Cahn–Hilliard-type
    equations on evolving surfaces. <i>Numerische Mathematik</i>. 2022;151(1):1-48.
    doi:<a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>
  apa: Beschle, C. A., &#38; Kovács, B. (2022). Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces. <i>Numerische Mathematik</i>,
    <i>151</i>(1), 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>
  bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
    non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>},
    number={1}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Beschle, Cedric Aaron and Kovács, Balázs}, year={2022}, pages={1–48}
    }'
  chicago: 'Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates
    for Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische
    Mathematik</i> 151, no. 1 (2022): 1–48. <a href="https://doi.org/10.1007/s00211-022-01280-5">https://doi.org/10.1007/s00211-022-01280-5</a>.'
  ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
    Cahn–Hilliard-type equations on evolving surfaces,” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, pp. 1–48, 2022, doi: <a href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.'
  mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
    Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” <i>Numerische Mathematik</i>,
    vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:<a
    href="https://doi.org/10.1007/s00211-022-01280-5">10.1007/s00211-022-01280-5</a>.
  short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: '       151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
  evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '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: '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: '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: '34631'
author:
- first_name: Kerstin
  full_name: Hesse, Kerstin
  id: '42608'
  last_name: Hesse
  orcid: 0000-0003-4125-1941
- first_name: Ian H.
  full_name: Sloan, Ian H.
  last_name: Sloan
- first_name: Robert S.
  full_name: Womersley, Robert S.
  last_name: Womersley
citation:
  ama: Hesse K, Sloan IH, Womersley RS. Radial basis function approximation of noisy
    scattered data on the sphere. <i>Numerische Mathematik</i>. 2017;137(3):579-605.
    doi:<a href="https://doi.org/10.1007/s00211-017-0886-6">10.1007/s00211-017-0886-6</a>
  apa: Hesse, K., Sloan, I. H., &#38; Womersley, R. S. (2017). Radial basis function
    approximation of noisy scattered data on the sphere. <i>Numerische Mathematik</i>,
    <i>137</i>(3), 579–605. <a href="https://doi.org/10.1007/s00211-017-0886-6">https://doi.org/10.1007/s00211-017-0886-6</a>
  bibtex: '@article{Hesse_Sloan_Womersley_2017, title={Radial basis function approximation
    of noisy scattered data on the sphere}, volume={137}, DOI={<a href="https://doi.org/10.1007/s00211-017-0886-6">10.1007/s00211-017-0886-6</a>},
    number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.},
    year={2017}, pages={579–605} }'
  chicago: 'Hesse, Kerstin, Ian H. Sloan, and Robert S. Womersley. “Radial Basis Function
    Approximation of Noisy Scattered Data on the Sphere.” <i>Numerische Mathematik</i>
    137, no. 3 (2017): 579–605. <a href="https://doi.org/10.1007/s00211-017-0886-6">https://doi.org/10.1007/s00211-017-0886-6</a>.'
  ieee: 'K. Hesse, I. H. Sloan, and R. S. Womersley, “Radial basis function approximation
    of noisy scattered data on the sphere,” <i>Numerische Mathematik</i>, vol. 137,
    no. 3, pp. 579–605, 2017, doi: <a href="https://doi.org/10.1007/s00211-017-0886-6">10.1007/s00211-017-0886-6</a>.'
  mla: Hesse, Kerstin, et al. “Radial Basis Function Approximation of Noisy Scattered
    Data on the Sphere.” <i>Numerische Mathematik</i>, vol. 137, no. 3, Springer Science
    and Business Media LLC, 2017, pp. 579–605, doi:<a href="https://doi.org/10.1007/s00211-017-0886-6">10.1007/s00211-017-0886-6</a>.
  short: K. Hesse, I.H. Sloan, R.S. Womersley, Numerische Mathematik 137 (2017) 579–605.
date_created: 2022-12-20T17:29:02Z
date_updated: 2023-01-09T08:24:20Z
department:
- _id: '10'
doi: 10.1007/s00211-017-0886-6
intvolume: '       137'
issue: '3'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 579-605
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Radial basis function approximation of noisy scattered data on the sphere
type: journal_article
user_id: '14931'
volume: 137
year: '2017'
...
---
_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: '16582'
author:
- first_name: F.
  full_name: Demoures, F.
  last_name: Demoures
- first_name: F.
  full_name: Gay-Balmaz, F.
  last_name: Gay-Balmaz
- first_name: S.
  full_name: Leyendecker, S.
  last_name: Leyendecker
- first_name: S.
  full_name: Ober-Blöbaum, S.
  last_name: Ober-Blöbaum
- first_name: T. S.
  full_name: Ratiu, T. S.
  last_name: Ratiu
- first_name: Y.
  full_name: Weinand, Y.
  last_name: Weinand
citation:
  ama: Demoures F, Gay-Balmaz F, Leyendecker S, Ober-Blöbaum S, Ratiu TS, Weinand
    Y. Discrete variational Lie group formulation of geometrically exact beam dynamics.
    <i>Numerische Mathematik</i>. 2015:73-123. doi:<a href="https://doi.org/10.1007/s00211-014-0659-4">10.1007/s00211-014-0659-4</a>
  apa: Demoures, F., Gay-Balmaz, F., Leyendecker, S., Ober-Blöbaum, S., Ratiu, T.
    S., &#38; Weinand, Y. (2015). Discrete variational Lie group formulation of geometrically
    exact beam dynamics. <i>Numerische Mathematik</i>, 73–123. <a href="https://doi.org/10.1007/s00211-014-0659-4">https://doi.org/10.1007/s00211-014-0659-4</a>
  bibtex: '@article{Demoures_Gay-Balmaz_Leyendecker_Ober-Blöbaum_Ratiu_Weinand_2015,
    title={Discrete variational Lie group formulation of geometrically exact beam
    dynamics}, DOI={<a href="https://doi.org/10.1007/s00211-014-0659-4">10.1007/s00211-014-0659-4</a>},
    journal={Numerische Mathematik}, author={Demoures, F. and Gay-Balmaz, F. and Leyendecker,
    S. and Ober-Blöbaum, S. and Ratiu, T. S. and Weinand, Y.}, year={2015}, pages={73–123}
    }'
  chicago: Demoures, F., F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu,
    and Y. Weinand. “Discrete Variational Lie Group Formulation of Geometrically Exact
    Beam Dynamics.” <i>Numerische Mathematik</i>, 2015, 73–123. <a href="https://doi.org/10.1007/s00211-014-0659-4">https://doi.org/10.1007/s00211-014-0659-4</a>.
  ieee: F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu,
    and Y. Weinand, “Discrete variational Lie group formulation of geometrically exact
    beam dynamics,” <i>Numerische Mathematik</i>, pp. 73–123, 2015.
  mla: Demoures, F., et al. “Discrete Variational Lie Group Formulation of Geometrically
    Exact Beam Dynamics.” <i>Numerische Mathematik</i>, 2015, pp. 73–123, doi:<a href="https://doi.org/10.1007/s00211-014-0659-4">10.1007/s00211-014-0659-4</a>.
  short: F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T.S. Ratiu,
    Y. Weinand, Numerische Mathematik (2015) 73–123.
date_created: 2020-04-16T05:40:13Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s00211-014-0659-4
language:
- iso: eng
page: 73-123
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
status: public
title: Discrete variational Lie group formulation of geometrically exact beam dynamics
type: journal_article
user_id: '15701'
year: '2015'
...
---
_id: '17015'
author:
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
- first_name: Andreas
  full_name: Hohmann, Andreas
  last_name: Hohmann
citation:
  ama: Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable
    manifolds and global attractors. <i>Numerische Mathematik</i>. 1997;75:293-317.
    doi:<a href="https://doi.org/10.1007/s002110050240">10.1007/s002110050240</a>
  apa: Dellnitz, M., &#38; Hohmann, A. (1997). A subdivision algorithm for the computation
    of unstable manifolds and global attractors. <i>Numerische Mathematik</i>, <i>75</i>,
    293–317. <a href="https://doi.org/10.1007/s002110050240">https://doi.org/10.1007/s002110050240</a>
  bibtex: '@article{Dellnitz_Hohmann_1997, title={A subdivision algorithm for the
    computation of unstable manifolds and global attractors}, volume={75}, DOI={<a
    href="https://doi.org/10.1007/s002110050240">10.1007/s002110050240</a>}, journal={Numerische
    Mathematik}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1997}, pages={293–317}
    }'
  chicago: 'Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the
    Computation of Unstable Manifolds and Global Attractors.” <i>Numerische Mathematik</i>
    75 (1997): 293–317. <a href="https://doi.org/10.1007/s002110050240">https://doi.org/10.1007/s002110050240</a>.'
  ieee: M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of
    unstable manifolds and global attractors,” <i>Numerische Mathematik</i>, vol.
    75, pp. 293–317, 1997.
  mla: Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation
    of Unstable Manifolds and Global Attractors.” <i>Numerische Mathematik</i>, vol.
    75, 1997, pp. 293–317, doi:<a href="https://doi.org/10.1007/s002110050240">10.1007/s002110050240</a>.
  short: M. Dellnitz, A. Hohmann, Numerische Mathematik 75 (1997) 293–317.
date_created: 2020-05-19T09:07:27Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.1007/s002110050240
intvolume: '        75'
language:
- iso: eng
page: 293-317
publication: Numerische Mathematik
publication_identifier:
  issn:
  - 0029-599X
  - 0945-3245
publication_status: published
status: public
title: A subdivision algorithm for the computation of unstable manifolds and global
  attractors
type: journal_article
user_id: '32643'
volume: 75
year: '1997'
...