---
_id: '45969'
abstract:
- lang: eng
text: 'AbstractAn 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$$H^1$$H1norm
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.'
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. Numerische Mathematik.
2022;151(4):873-925. doi:10.1007/s00211-022-01301-3
apa: Elliott, C. M., Garcke, H., & Kovács, B. (2022). Numerical analysis for
the interaction of mean curvature flow and diffusion on closed surfaces. Numerische
Mathematik, 151(4), 873–925. https://doi.org/10.1007/s00211-022-01301-3
bibtex: '@article{Elliott_Garcke_Kovács_2022, title={Numerical analysis for the
interaction of mean curvature flow and diffusion on closed surfaces}, volume={151},
DOI={10.1007/s00211-022-01301-3},
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.”
Numerische Mathematik 151, no. 4 (2022): 873–925. https://doi.org/10.1007/s00211-022-01301-3.'
ieee: 'C. M. Elliott, H. Garcke, and B. Kovács, “Numerical analysis for the interaction
of mean curvature flow and diffusion on closed surfaces,” Numerische Mathematik,
vol. 151, no. 4, pp. 873–925, 2022, doi: 10.1007/s00211-022-01301-3.'
mla: Elliott, Charles M., et al. “Numerical Analysis for the Interaction of Mean
Curvature Flow and Diffusion on Closed Surfaces.” Numerische Mathematik,
vol. 151, no. 4, Springer Science and Business Media LLC, 2022, pp. 873–925, doi:10.1007/s00211-022-01301-3.
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: AbstractThe 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.
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. Numerische Mathematik. 2022;150(4):1123-1164. doi:10.1007/s00211-022-01277-0
apa: Nick, J., Kovács, B., & Lubich, C. (2022). Time-dependent electromagnetic
scattering from thin layers. Numerische Mathematik, 150(4), 1123–1164.
https://doi.org/10.1007/s00211-022-01277-0
bibtex: '@article{Nick_Kovács_Lubich_2022, title={Time-dependent electromagnetic
scattering from thin layers}, volume={150}, DOI={10.1007/s00211-022-01277-0},
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.” Numerische Mathematik 150, no. 4 (2022):
1123–64. https://doi.org/10.1007/s00211-022-01277-0.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Time-dependent electromagnetic scattering
from thin layers,” Numerische Mathematik, vol. 150, no. 4, pp. 1123–1164,
2022, doi: 10.1007/s00211-022-01277-0.'
mla: Nick, Jörg, et al. “Time-Dependent Electromagnetic Scattering from Thin Layers.”
Numerische Mathematik, vol. 150, no. 4, Springer Science and Business Media
LLC, 2022, pp. 1123–64, doi:10.1007/s00211-022-01277-0.
short: J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 150 (2022) 1123–1164.
date_created: 2023-07-10T11:44:57Z
date_updated: 2024-04-03T09:18:23Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01277-0
intvolume: ' 150'
issue: '4'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1123-1164
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Time-dependent electromagnetic scattering from thin layers
type: journal_article
user_id: '100441'
volume: 150
year: '2022'
...
---
_id: '45964'
abstract:
- lang: eng
text: "Abstract\r\n Maximal parabolic
$L^p$-regularity of linear parabolic equations on an evolving surface is shown
by pulling back the problem to the initial surface and studying the maximal $L^p$-regularity
on a fixed surface. By freezing the coefficients in the parabolic equations at
a fixed time and utilizing a perturbation argument around the freezed time, it
is shown that backward difference time discretizations of linear parabolic equations
on an evolving surface along characteristic trajectories can preserve maximal
$L^p$-regularity in the discrete setting. The result is applied to prove the stability
and convergence of time discretizations of nonlinear parabolic equations on an
evolving surface, with linearly implicit backward differentiation formulae characteristic
trajectories of the surface, for general locally Lipschitz nonlinearities. The
discrete maximal $L^p$-regularity is used to prove the boundedness and stability
of numerical solutions in the $L^\\infty (0,T;W^{1,\\infty })$ norm, which is
used to bound the nonlinear terms in the stability analysis. Optimal-order error
estimates of time discretizations in the $L^\\infty (0,T;W^{1,\\infty })$ norm
is obtained by combining the stability analysis with the consistency estimates."
author:
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Buyang
full_name: Li, Buyang
last_name: Li
citation:
ama: Kovács B, Li B. Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems. IMA Journal
of Numerical Analysis. Published online 2022. doi:10.1093/imanum/drac033
apa: Kovács, B., & Li, B. (2022). Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems. IMA Journal of Numerical Analysis. https://doi.org/10.1093/imanum/drac033
bibtex: '@article{Kovács_Li_2022, title={Maximal regularity of backward difference
time discretization for evolving surface PDEs and its application to nonlinear
problems}, DOI={10.1093/imanum/drac033},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Kovács, Balázs and Li, Buyang}, year={2022} }'
chicago: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference
Time Discretization for Evolving Surface PDEs and Its Application to Nonlinear
Problems.” IMA Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac033.
ieee: 'B. Kovács and B. Li, “Maximal regularity of backward difference time discretization
for evolving surface PDEs and its application to nonlinear problems,” IMA Journal
of Numerical Analysis, 2022, doi: 10.1093/imanum/drac033.'
mla: Kovács, Balázs, and Buyang Li. “Maximal Regularity of Backward Difference Time
Discretization for Evolving Surface PDEs and Its Application to Nonlinear Problems.”
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2022,
doi:10.1093/imanum/drac033.
short: B. Kovács, B. Li, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:45:14Z
date_updated: 2024-04-03T09:17:59Z
department:
- _id: '841'
doi: 10.1093/imanum/drac033
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Maximal regularity of backward difference time discretization for evolving
surface PDEs and its application to nonlinear problems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45966'
abstract:
- lang: eng
text: "Abstract\r\n This paper studies
bulk–surface splitting methods of first order for (semilinear) parabolic partial
differential equations with dynamic boundary conditions. The proposed Lie splitting
scheme is based on a reformulation of the problem as a coupled partial differential–algebraic
equation system, i.e., the boundary conditions are considered as a second dynamic
equation that is coupled to the bulk problem. The splitting approach is combined
with bulk–surface finite elements and an implicit Euler discretization of the
two subsystems. We prove first-order convergence of the resulting fully discrete
scheme in the presence of a weak CFL condition of the form $\\tau \\leqslant c
h$ for some constant $c>0$. The convergence is also illustrated numerically
using dynamic boundary conditions of Allen–Cahn type."
author:
- first_name: Robert
full_name: Altmann, Robert
last_name: Altmann
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
- first_name: Christoph
full_name: Zimmer, Christoph
last_name: Zimmer
citation:
ama: Altmann R, Kovács B, Zimmer C. Bulk–surface Lie splitting for parabolic problems
with dynamic boundary conditions. IMA Journal of Numerical Analysis. 2022;43(2):950-975.
doi:10.1093/imanum/drac002
apa: Altmann, R., Kovács, B., & Zimmer, C. (2022). Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions. IMA Journal of Numerical
Analysis, 43(2), 950–975. https://doi.org/10.1093/imanum/drac002
bibtex: '@article{Altmann_Kovács_Zimmer_2022, title={Bulk–surface Lie splitting
for parabolic problems with dynamic boundary conditions}, volume={43}, DOI={10.1093/imanum/drac002}, number={2},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Altmann, Robert and Kovács, Balázs and Zimmer, Christoph}, year={2022},
pages={950–975} }'
chicago: 'Altmann, Robert, Balázs Kovács, and Christoph Zimmer. “Bulk–Surface Lie
Splitting for Parabolic Problems with Dynamic Boundary Conditions.” IMA Journal
of Numerical Analysis 43, no. 2 (2022): 950–75. https://doi.org/10.1093/imanum/drac002.'
ieee: 'R. Altmann, B. Kovács, and C. Zimmer, “Bulk–surface Lie splitting for parabolic
problems with dynamic boundary conditions,” IMA Journal of Numerical Analysis,
vol. 43, no. 2, pp. 950–975, 2022, doi: 10.1093/imanum/drac002.'
mla: Altmann, Robert, et al. “Bulk–Surface Lie Splitting for Parabolic Problems
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
43, no. 2, Oxford University Press (OUP), 2022, pp. 950–75, doi:10.1093/imanum/drac002.
short: R. Altmann, B. Kovács, C. Zimmer, IMA Journal of Numerical Analysis 43 (2022)
950–975.
date_created: 2023-07-10T11:45:49Z
date_updated: 2024-04-03T09:16:47Z
department:
- _id: '841'
doi: 10.1093/imanum/drac002
intvolume: ' 43'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 950-975
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Bulk–surface Lie splitting for parabolic problems with dynamic boundary conditions
type: journal_article
user_id: '100441'
volume: 43
year: '2022'
...
---
_id: '45968'
abstract:
- lang: eng
text: "Abstract\r\n We derive a numerical
method, based on operator splitting, to abstract parabolic semilinear boundary
coupled systems. The method decouples the linear components that describe the
coupling and the dynamics in the abstract bulk- and surface-spaces, and treats
the nonlinear terms similarly to an exponential integrator. The convergence proof
is based on estimates for a recursive formulation of the error, using the parabolic
smoothing property of analytic semigroups, and a careful comparison of the exact
and approximate flows. This analysis also requires a deep understanding of the
effects of the Dirichlet operator (the abstract version of the harmonic extension
operator), which is essential for the stable coupling in our method. Numerical
experiments, including problems with dynamic boundary conditions, reporting on
convergence rates are presented."
author:
- first_name: Petra
full_name: Csomós, Petra
last_name: Csomós
- first_name: Bálint
full_name: Farkas, Bálint
last_name: Farkas
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Csomós P, Farkas B, Kovács B. Error estimates for a splitting integrator for
abstract semilinear boundary coupled systems. IMA Journal of Numerical Analysis.
Published online 2022. doi:10.1093/imanum/drac079
apa: Csomós, P., Farkas, B., & Kovács, B. (2022). Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems. IMA Journal of
Numerical Analysis. https://doi.org/10.1093/imanum/drac079
bibtex: '@article{Csomós_Farkas_Kovács_2022, title={Error estimates for a splitting
integrator for abstract semilinear boundary coupled systems}, DOI={10.1093/imanum/drac079},
journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press
(OUP)}, author={Csomós, Petra and Farkas, Bálint and Kovács, Balázs}, year={2022}
}'
chicago: Csomós, Petra, Bálint Farkas, and Balázs Kovács. “Error Estimates for a
Splitting Integrator for Abstract Semilinear Boundary Coupled Systems.” IMA
Journal of Numerical Analysis, 2022. https://doi.org/10.1093/imanum/drac079.
ieee: 'P. Csomós, B. Farkas, and B. Kovács, “Error estimates for a splitting integrator
for abstract semilinear boundary coupled systems,” IMA Journal of Numerical
Analysis, 2022, doi: 10.1093/imanum/drac079.'
mla: Csomós, Petra, et al. “Error Estimates for a Splitting Integrator for Abstract
Semilinear Boundary Coupled Systems.” IMA Journal of Numerical Analysis,
Oxford University Press (OUP), 2022, doi:10.1093/imanum/drac079.
short: P. Csomós, B. Farkas, B. Kovács, IMA Journal of Numerical Analysis (2022).
date_created: 2023-07-10T11:46:54Z
date_updated: 2024-04-03T09:15:52Z
department:
- _id: '841'
doi: 10.1093/imanum/drac079
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Error estimates for a splitting integrator for abstract semilinear boundary
coupled systems
type: journal_article
user_id: '100441'
year: '2022'
...
---
_id: '45958'
abstract:
- lang: eng
text: AbstractIn 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.
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. Numerische Mathematik. 2022;151(1):1-48.
doi:10.1007/s00211-022-01280-5
apa: Beschle, C. A., & Kovács, B. (2022). Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces. Numerische Mathematik,
151(1), 1–48. https://doi.org/10.1007/s00211-022-01280-5
bibtex: '@article{Beschle_Kovács_2022, title={Stability and error estimates for
non-linear Cahn–Hilliard-type equations on evolving surfaces}, volume={151}, DOI={10.1007/s00211-022-01280-5},
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.” Numerische
Mathematik 151, no. 1 (2022): 1–48. https://doi.org/10.1007/s00211-022-01280-5.'
ieee: 'C. A. Beschle and B. Kovács, “Stability and error estimates for non-linear
Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik,
vol. 151, no. 1, pp. 1–48, 2022, doi: 10.1007/s00211-022-01280-5.'
mla: Beschle, Cedric Aaron, and Balázs Kovács. “Stability and Error Estimates for
Non-Linear Cahn–Hilliard-Type Equations on Evolving Surfaces.” Numerische Mathematik,
vol. 151, no. 1, Springer Science and Business Media LLC, 2022, pp. 1–48, doi:10.1007/s00211-022-01280-5.
short: C.A. Beschle, B. Kovács, Numerische Mathematik 151 (2022) 1–48.
date_created: 2023-07-10T11:43:44Z
date_updated: 2024-04-03T09:19:34Z
department:
- _id: '841'
doi: 10.1007/s00211-022-01280-5
intvolume: ' 151'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
language:
- iso: eng
page: 1-48
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Stability and error estimates for non-linear Cahn–Hilliard-type equations on
evolving surfaces
type: journal_article
user_id: '100441'
volume: 151
year: '2022'
...
---
_id: '45956'
abstract:
- lang: eng
text: "Abstract\r\n The full Maxwell
equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert
equation serve as a well-tested model for ferromagnetic materials.\r\nWe propose
a weak formulation of the coupled system based on the boundary integral formulation
of the exterior Maxwell equations.\r\nWe show existence and partial uniqueness
of a weak solution and propose a new numerical algorithm based on finite elements
and boundary elements as spatial discretization with backward Euler and convolution
quadrature for the time domain.\r\nThis is the first numerical algorithm which
is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and
full Maxwell’s equations without any simplifications like quasi-static approximations
(e.g. eddy current model) and without restrictions on the shape of the domain
(e.g. convexity).\r\nWe show well-posedness and convergence of the numerical algorithm
under minimal assumptions on the regularity of the solution.\r\nThis is particularly
important as there are few regularity results available and one generally expects
the solution to be non-smooth.\r\nNumerical experiments illustrate and expand
on the theoretical results."
author:
- first_name: Jan
full_name: Bohn, Jan
last_name: Bohn
- first_name: Michael
full_name: Feischl, Michael
last_name: Feischl
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: 'Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics. 2022;23(1):19-48. doi:10.1515/cmam-2022-0145'
apa: 'Bohn, J., Feischl, M., & Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation. Computational
Methods in Applied Mathematics, 23(1), 19–48. https://doi.org/10.1515/cmam-2022-0145'
bibtex: '@article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation},
volume={23}, DOI={10.1515/cmam-2022-0145},
number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter
de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs},
year={2022}, pages={19–48} }'
chicago: 'Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the
Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form
and Numerical Approximation.” Computational Methods in Applied Mathematics
23, no. 1 (2022): 19–48. https://doi.org/10.1515/cmam-2022-0145.'
ieee: 'J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation,”
Computational Methods in Applied Mathematics, vol. 23, no. 1, pp. 19–48,
2022, doi: 10.1515/cmam-2022-0145.'
mla: 'Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert
Equations via Convolution Quadrature: Weak Form and Numerical Approximation.”
Computational Methods in Applied Mathematics, vol. 23, no. 1, Walter de
Gruyter GmbH, 2022, pp. 19–48, doi:10.1515/cmam-2022-0145.'
short: J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics
23 (2022) 19–48.
date_created: 2023-07-10T11:43:13Z
date_updated: 2024-04-03T09:20:30Z
department:
- _id: '841'
doi: 10.1515/cmam-2022-0145
intvolume: ' 23'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis
language:
- iso: eng
page: 19-48
publication: Computational Methods in Applied Mathematics
publication_identifier:
issn:
- 1609-4840
- 1609-9389
publication_status: published
publisher: Walter de Gruyter GmbH
status: public
title: 'FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution
Quadrature: Weak Form and Numerical Approximation'
type: journal_article
user_id: '100441'
volume: 23
year: '2022'
...
---
_id: '45967'
author:
- first_name: Tim
full_name: Binz, Tim
last_name: Binz
- first_name: Balázs
full_name: Kovács, Balázs
id: '100441'
last_name: Kovács
orcid: 0000-0001-9872-3474
citation:
ama: Binz T, Kovács B. A convergent finite element algorithm for mean curvature
flow in higher codimension. arXiv. Published online 2021.
apa: Binz, T., & Kovács, B. (2021). A convergent finite element algorithm for
mean curvature flow in higher codimension. ArXiv.
bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
for mean curvature flow in higher codimension}, journal={arXiv}, author={Binz,
Tim and Kovács, Balázs}, year={2021} }'
chicago: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for
Mean Curvature Flow in Higher Codimension.” ArXiv, 2021.
ieee: T. Binz and B. Kovács, “A convergent finite element algorithm for mean curvature
flow in higher codimension,” arXiv, 2021.
mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean
Curvature Flow in Higher Codimension.” ArXiv, 2021.
short: T. Binz, B. Kovács, ArXiv (2021).
date_created: 2023-07-10T11:46:16Z
date_updated: 2024-04-03T09:16:19Z
department:
- _id: '841'
language:
- iso: eng
publication: arXiv
status: public
title: A convergent finite element algorithm for mean curvature flow in higher codimension
type: journal_article
user_id: '100441'
year: '2021'
...
---
_id: '45962'
abstract:
- lang: eng
text: "Abstract\r\n 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."
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. IMA Journal of Numerical Analysis.
2021;42(3):2545-2588. doi:10.1093/imanum/drab043
apa: Binz, T., & Kovács, B. (2021). A convergent finite element algorithm for
generalized mean curvature flows of closed surfaces. IMA Journal of Numerical
Analysis, 42(3), 2545–2588. https://doi.org/10.1093/imanum/drab043
bibtex: '@article{Binz_Kovács_2021, title={A convergent finite element algorithm
for generalized mean curvature flows of closed surfaces}, volume={42}, DOI={10.1093/imanum/drab043}, 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.” IMA Journal of Numerical
Analysis 42, no. 3 (2021): 2545–88. https://doi.org/10.1093/imanum/drab043.'
ieee: 'T. Binz and B. Kovács, “A convergent finite element algorithm for generalized
mean curvature flows of closed surfaces,” IMA Journal of Numerical Analysis,
vol. 42, no. 3, pp. 2545–2588, 2021, doi: 10.1093/imanum/drab043.'
mla: Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized
Mean Curvature Flows of Closed Surfaces.” IMA Journal of Numerical Analysis,
vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2545–88, doi:10.1093/imanum/drab043.
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: AbstractA 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.
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. IMA Journal of Numerical Analysis. 2021;42(3):2589-2620.
doi:10.1093/imanum/drab045
apa: Harder, P., & Kovács, B. (2021). Error estimates for the Cahn–Hilliard
equation with dynamic boundary conditions. IMA Journal of Numerical Analysis,
42(3), 2589–2620. https://doi.org/10.1093/imanum/drab045
bibtex: '@article{Harder_Kovács_2021, title={Error estimates for the Cahn–Hilliard
equation with dynamic boundary conditions}, volume={42}, DOI={10.1093/imanum/drab045},
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.” IMA Journal of Numerical Analysis
42, no. 3 (2021): 2589–2620. https://doi.org/10.1093/imanum/drab045.'
ieee: 'P. Harder and B. Kovács, “Error estimates for the Cahn–Hilliard equation
with dynamic boundary conditions,” IMA Journal of Numerical Analysis, vol.
42, no. 3, pp. 2589–2620, 2021, doi: 10.1093/imanum/drab045.'
mla: Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation
with Dynamic Boundary Conditions.” IMA Journal of Numerical Analysis, vol.
42, no. 3, Oxford University Press (OUP), 2021, pp. 2589–620, doi:10.1093/imanum/drab045.
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. Numerische Mathematik.
2021;147(4):997-1000. doi:10.1007/s00211-021-01196-6'
apa: 'Nick, J., Kovács, B., & Lubich, C. (2021). Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations. Numerische
Mathematik, 147(4), 997–1000. https://doi.org/10.1007/s00211-021-01196-6'
bibtex: '@article{Nick_Kovács_Lubich_2021, title={Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations}, volume={147},
DOI={10.1007/s00211-021-01196-6},
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.”
Numerische Mathematik 147, no. 4 (2021): 997–1000. https://doi.org/10.1007/s00211-021-01196-6.'
ieee: 'J. Nick, B. Kovács, and C. Lubich, “Correction to: Stable and convergent
fully discrete interior–exterior coupling of Maxwell’s equations,” Numerische
Mathematik, vol. 147, no. 4, pp. 997–1000, 2021, doi: 10.1007/s00211-021-01196-6.'
mla: 'Nick, Jörg, et al. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior
Coupling of Maxwell’s Equations.” Numerische Mathematik, vol. 147, no.
4, Springer Science and Business Media LLC, 2021, pp. 997–1000, doi:10.1007/s00211-021-01196-6.'
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: '33273'
abstract:
- lang: ger
text: "Dieses Lernangebot widmet sich der linearen Algebra als dem Teil der Mathematik,
der neben der Optimierung und der Stochastik die Grundlage für praktisch alle
Entwicklungen im Bereich Künstliche Intelligenz (KI) darstellt. Das Fach ist jedoch
für Anfänger meist ungewohnt abstrakt und wird daher oft als besonders schwierig
und unanschaulich empfunden. In diesem Kurs wird das Erlernen mathematischer Kenntnisse
in linearer Algebra verknüpft mit dem aktuellen und faszinierenden Anwendungsfeld
der künstlichen neuronalen Netze (KNN). Daraus ergeben sich in natürlicher Weise
Anwendungsbeispiele, an denen die wesentlichen Konzepte der linearen Algebra erklärt
werden können.\r\n\r\nBehandelte Themen sind:\r\n\r\n Der Vektorraum der reellen
Zahlentupel, reelle Vektorräume allgemein\r\n Lineare Abbildungen\r\n Matrizen\r\n
\ Koordinaten und darstellende Matrizen\r\n Lineare Gleichungssysteme, Gaußalgorithmus\r\n
\ Determinante\r\n Ein Ausblick auf nichtlineare Techniken, die für neuronale
Netzwerke relevant sind."
author:
- first_name: Thomas
full_name: Schramm, Thomas
last_name: Schramm
- first_name: Ingenuin
full_name: Gasser, Ingenuin
last_name: Gasser
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
- first_name: Ruedi
full_name: Seiler, Ruedi
last_name: Seiler
- first_name: Alexander
full_name: Lohse, Alexander
last_name: Lohse
- first_name: Kay
full_name: Zobel, Kay
last_name: Zobel
citation:
ama: Schramm T, Gasser I, Schwenker S, Seiler R, Lohse A, Zobel K. Linear Algebra
Driven by Data Science. Hamburg Open Online University; 2020.
apa: Schramm, T., Gasser, I., Schwenker, S., Seiler, R., Lohse, A., & Zobel,
K. (2020). Linear Algebra driven by Data Science. Hamburg Open Online University.
bibtex: '@book{Schramm_Gasser_Schwenker_Seiler_Lohse_Zobel_2020, title={Linear Algebra
driven by Data Science}, publisher={Hamburg Open Online University}, author={Schramm,
Thomas and Gasser, Ingenuin and Schwenker, Sören and Seiler, Ruedi and Lohse,
Alexander and Zobel, Kay}, year={2020} }'
chicago: Schramm, Thomas, Ingenuin Gasser, Sören Schwenker, Ruedi Seiler, Alexander
Lohse, and Kay Zobel. Linear Algebra Driven by Data Science. Hamburg Open
Online University, 2020.
ieee: T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, and K. Zobel, Linear
Algebra driven by Data Science. Hamburg Open Online University, 2020.
mla: Schramm, Thomas, et al. Linear Algebra Driven by Data Science. Hamburg
Open Online University, 2020.
short: T. Schramm, I. Gasser, S. Schwenker, R. Seiler, A. Lohse, K. Zobel, Linear
Algebra Driven by Data Science, Hamburg Open Online University, 2020.
date_created: 2022-09-06T12:06:41Z
date_updated: 2022-09-06T14:05:13Z
department:
- _id: '94'
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://www.hoou.de/projects/linear-algebra-driven-by-data-science/
publisher: Hamburg Open Online University
status: public
title: Linear Algebra driven by Data Science
type: misc
user_id: '97359'
year: '2020'
...
---
_id: '33272'
author:
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
citation:
ama: Nijholt E, Rink B, Schwenker S. Generalised Symmetry in Network Dynamics. DSWeb.
2020.
apa: Nijholt, E., Rink, B., & Schwenker, S. (2020). Generalised Symmetry in
Network Dynamics. DSWeb, April.
bibtex: '@article{Nijholt_Rink_Schwenker_2020, title={Generalised Symmetry in Network
Dynamics}, number={April}, journal={DSWeb}, author={Nijholt, Eddie and Rink, Bob
and Schwenker, Sören}, year={2020} }'
chicago: Nijholt, Eddie, Bob Rink, and Sören Schwenker. “Generalised Symmetry in
Network Dynamics.” DSWeb, 2020.
ieee: E. Nijholt, B. Rink, and S. Schwenker, “Generalised Symmetry in Network Dynamics,”
DSWeb, no. April, 2020.
mla: Nijholt, Eddie, et al. “Generalised Symmetry in Network Dynamics.” DSWeb,
no. April, 2020.
short: E. Nijholt, B. Rink, S. Schwenker, DSWeb (2020).
date_created: 2022-09-06T11:46:58Z
date_updated: 2022-09-06T14:05:35Z
extern: '1'
issue: April
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://dsweb.siam.org/The-Magazine/Article/generalised-symmetry-in-network-dynamics
oa: '1'
publication: DSWeb
publication_date: 2020-04.30
status: public
title: Generalised Symmetry in Network Dynamics
type: newspaper_article
user_id: '97359'
year: '2020'
...
---
_id: '33262'
abstract:
- lang: eng
text: The authors of Berg et al. [J. Algebra 348 (2011) 446–461] provide an algorithm
for finding a complete system of primitive orthogonal idempotents for CM, where
M is any finite R-trivial monoid. Their method relies on a technical result stating
that R-trivial monoid are equivalent to so-called weakly ordered monoids. We provide
an alternative algorithm, based only on the simple observation that an R-trivial
monoid may be realized by upper triangular matrices. This approach is inspired
by results in the field of coupled cell network dynamical systems, where L-trivial
monoids (the opposite notion) correspond to so-called feed-forward networks. We
first show that our algorithm works for ZM, after which we prove that it also
works for RM where R is an arbitrary ring with a known complete system of primitive
orthogonal idempotents. In particular, our algorithm works if R is any field.
In this respect our result constitutes a considerable generalization of the results
in Berg et al. [J. Algebra 348 (2011) 446–461]. Moreover, the system of idempotents
for RM is obtained from the one our algorithm yields for ZM in a straightforward
manner. In other words, for any finite R-trivial monoid M our algorithm only has
to be performed for ZM, after which a system of idempotents follows for any ring
with a given system of idempotents.
author:
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
citation:
ama: Nijholt E, Rink B, Schwenker S. A new algorithm for computing idempotents of
ℛ-trivial monoids. Journal of Algebra and Its Applications. 2020;20(12).
doi:10.1142/s0219498821502273
apa: Nijholt, E., Rink, B., & Schwenker, S. (2020). A new algorithm for computing
idempotents of ℛ-trivial monoids. Journal of Algebra and Its Applications,
20(12). https://doi.org/10.1142/s0219498821502273
bibtex: '@article{Nijholt_Rink_Schwenker_2020, title={A new algorithm for computing
idempotents of ℛ-trivial monoids}, volume={20}, DOI={10.1142/s0219498821502273},
number={12}, journal={Journal of Algebra and Its Applications}, publisher={World
Scientific Pub Co Pte Ltd}, author={Nijholt, Eddie and Rink, Bob and Schwenker,
Sören}, year={2020} }'
chicago: Nijholt, Eddie, Bob Rink, and Sören Schwenker. “A New Algorithm for Computing
Idempotents of ℛ-Trivial Monoids.” Journal of Algebra and Its Applications
20, no. 12 (2020). https://doi.org/10.1142/s0219498821502273.
ieee: 'E. Nijholt, B. Rink, and S. Schwenker, “A new algorithm for computing idempotents
of ℛ-trivial monoids,” Journal of Algebra and Its Applications, vol. 20,
no. 12, 2020, doi: 10.1142/s0219498821502273.'
mla: Nijholt, Eddie, et al. “A New Algorithm for Computing Idempotents of ℛ-Trivial
Monoids.” Journal of Algebra and Its Applications, vol. 20, no. 12, World
Scientific Pub Co Pte Ltd, 2020, doi:10.1142/s0219498821502273.
short: E. Nijholt, B. Rink, S. Schwenker, Journal of Algebra and Its Applications
20 (2020).
date_created: 2022-09-06T11:37:00Z
date_updated: 2022-09-07T08:35:24Z
doi: 10.1142/s0219498821502273
extern: '1'
external_id:
arxiv:
- '1906.02844'
intvolume: ' 20'
issue: '12'
keyword:
- Applied Mathematics
- Algebra and Number Theory
language:
- iso: eng
publication: Journal of Algebra and Its Applications
publication_identifier:
issn:
- 0219-4988
- 1793-6829
publication_status: published
publisher: World Scientific Pub Co Pte Ltd
status: public
title: A new algorithm for computing idempotents of ℛ-trivial monoids
type: journal_article
user_id: '97359'
volume: 20
year: '2020'
...
---
_id: '33263'
abstract:
- lang: eng
text: Dynamical systems often admit geometric properties that must be taken into
account when studying their behavior. We show that many such properties can be
encoded by means of quiver representations. These properties include classical
symmetry, hidden symmetry, and feedforward structure, as well as subnetwork and
quotient relations in network dynamical systems. A quiver equivariant dynamical
system consists of a collection of dynamical systems with maps between them that
send solutions to solutions. We prove that such quiver structures are preserved
under Lyapunov--Schmidt reduction, center manifold reduction, and normal form
reduction.
author:
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob W.
full_name: Rink, Bob W.
last_name: Rink
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
citation:
ama: Nijholt E, Rink BW, Schwenker S. Quiver Representations and Dimension Reduction
in Dynamical Systems. SIAM Journal on Applied Dynamical Systems. 2020;19(4):2428-2468.
doi:10.1137/20m1345670
apa: Nijholt, E., Rink, B. W., & Schwenker, S. (2020). Quiver Representations
and Dimension Reduction in Dynamical Systems. SIAM Journal on Applied Dynamical
Systems, 19(4), 2428–2468. https://doi.org/10.1137/20m1345670
bibtex: '@article{Nijholt_Rink_Schwenker_2020, title={Quiver Representations and
Dimension Reduction in Dynamical Systems}, volume={19}, DOI={10.1137/20m1345670},
number={4}, journal={SIAM Journal on Applied Dynamical Systems}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={Nijholt, Eddie and Rink,
Bob W. and Schwenker, Sören}, year={2020}, pages={2428–2468} }'
chicago: 'Nijholt, Eddie, Bob W. Rink, and Sören Schwenker. “Quiver Representations
and Dimension Reduction in Dynamical Systems.” SIAM Journal on Applied Dynamical
Systems 19, no. 4 (2020): 2428–68. https://doi.org/10.1137/20m1345670.'
ieee: 'E. Nijholt, B. W. Rink, and S. Schwenker, “Quiver Representations and Dimension
Reduction in Dynamical Systems,” SIAM Journal on Applied Dynamical Systems,
vol. 19, no. 4, pp. 2428–2468, 2020, doi: 10.1137/20m1345670.'
mla: Nijholt, Eddie, et al. “Quiver Representations and Dimension Reduction in Dynamical
Systems.” SIAM Journal on Applied Dynamical Systems, vol. 19, no. 4, Society
for Industrial & Applied Mathematics (SIAM), 2020, pp. 2428–68, doi:10.1137/20m1345670.
short: E. Nijholt, B.W. Rink, S. Schwenker, SIAM Journal on Applied Dynamical Systems
19 (2020) 2428–2468.
date_created: 2022-09-06T11:37:42Z
date_updated: 2022-09-07T08:36:03Z
doi: 10.1137/20m1345670
extern: '1'
external_id:
arxiv:
- '2006.08073'
intvolume: ' 19'
issue: '4'
keyword:
- Modeling and Simulation
- Analysis
language:
- iso: eng
page: 2428-2468
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: Quiver Representations and Dimension Reduction in Dynamical Systems
type: journal_article
user_id: '97359'
volume: 19
year: '2020'
...
---
_id: '45953'
abstract:
- lang: eng
text: "Abstract\r\n $L^2$ 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."
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: L2 estimates. IMA Journal of Numerical Analysis.
2020;41(1):638-728. doi:10.1093/imanum/drz073'
apa: 'Hipp, D., & Kovács, B. (2020). Finite element error analysis of wave equations
with dynamic boundary conditions: L2 estimates. IMA Journal of Numerical
Analysis, 41(1), 638–728. https://doi.org/10.1093/imanum/drz073'
bibtex: '@article{Hipp_Kovács_2020, title={Finite element error analysis of wave
equations with dynamic boundary conditions: L2 estimates}, volume={41},
DOI={10.1093/imanum/drz073},
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: L2 Estimates.” IMA Journal
of Numerical Analysis 41, no. 1 (2020): 638–728. https://doi.org/10.1093/imanum/drz073.'
ieee: 'D. Hipp and B. Kovács, “Finite element error analysis of wave equations with
dynamic boundary conditions: L2 estimates,” IMA Journal of Numerical
Analysis, vol. 41, no. 1, pp. 638–728, 2020, doi: 10.1093/imanum/drz073.'
mla: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations
with Dynamic Boundary Conditions: L2 Estimates.” IMA Journal of Numerical
Analysis, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728,
doi:10.1093/imanum/drz073.'
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:
L2 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. Mathematics of Computation.
2020;90(329):995-1038. doi:10.1090/mcom/3597
apa: Akrivis, G., Feischl, M., Kovács, B., & Lubich, C. (2020). Higher-order
linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation.
Mathematics of Computation, 90(329), 995–1038. https://doi.org/10.1090/mcom/3597
bibtex: '@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly
implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90},
DOI={10.1090/mcom/3597}, 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.” Mathematics of Computation 90, no. 329 (2020): 995–1038. https://doi.org/10.1090/mcom/3597.'
ieee: 'G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly
implicit full discretization of the Landau–Lifshitz–Gilbert equation,” Mathematics
of Computation, vol. 90, no. 329, pp. 995–1038, 2020, doi: 10.1090/mcom/3597.'
mla: Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization
of the Landau–Lifshitz–Gilbert Equation.” Mathematics of Computation, vol.
90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:10.1090/mcom/3597.
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. Interfaces and Free Boundaries.
2020;22(4):443-464. doi:10.4171/ifb/446
apa: Kovács, B., Li, B., & Lubich, C. (2020). A convergent algorithm for forced
mean curvature flow driven by diffusion on the surface. Interfaces and Free
Boundaries, 22(4), 443–464. https://doi.org/10.4171/ifb/446
bibtex: '@article{Kovács_Li_Lubich_2020, title={A convergent algorithm for forced
mean curvature flow driven by diffusion on the surface}, volume={22}, DOI={10.4171/ifb/446}, 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.” Interfaces
and Free Boundaries 22, no. 4 (2020): 443–64. https://doi.org/10.4171/ifb/446.'
ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent algorithm for forced mean
curvature flow driven by diffusion on the surface,” Interfaces and Free Boundaries,
vol. 22, no. 4, pp. 443–464, 2020, doi: 10.4171/ifb/446.'
mla: Kovács, Balázs, et al. “A Convergent Algorithm for Forced Mean Curvature Flow
Driven by Diffusion on the Surface.” Interfaces and Free Boundaries, vol.
22, no. 4, European Mathematical Society - EMS - Publishing House GmbH, 2020,
pp. 443–64, doi:10.4171/ifb/446.
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: '33265'
abstract:
- lang: eng
text: "This thesis deals with the investigation of dynamical properties – in particular
generic synchrony breaking bifurcations – that are inherent to the structure of
a semigroup network as well the numerous algebraic structures that are related
to these types of networks. Most notably we investigate the interplay between
network dynamics and monoid representation theory as induced by the fundamental
network construction in terms of hidden symmetry as introduced by RINK and SANDERS.\r\n\r\nAfter
providing a brief survey of the field of network dynamics in Part I, we thoroughly
introduce the formalism of semigroup networks, the customized dynamical systems
theory, and the necessary background from monoid representation theory in Chapters
3 and 4. The remainder of Part II investigates generic synchrony breaking bifurcations
and contains three major results. The first is Theorem 5.11, which shows that
generic symmetry breaking steady state bifurcations in monoid equivariant dynamics
occur along absolutely indecomposable subrepresentations – a natural generalization
of the corresponding statement for group equivariant dynamics. Then Theorem 7.12
relates the decomposition of a representation given by a network with high-dimensional
internal phase spaces to that induced by the same network with one-dimensional
internal phase spaces. This result is used to show that there is a smallest dimension
of internal dynamics in which all generic l-parameter bifurcations of a fundamental
network can be observed (Theorem 7.24).\r\n\r\nIn Part III, we employ the machinery
that was summarized and further developed in Part II to feedforward networks.
We propose a general definition of this structural feature of a network and show
that it can equivalently be characterized in different algebraic notions in Theorem
8.35. These are then exploited to fully classify the corresponding monoid representation
for any feedforward network and to classify generic synchrony breaking steady
state bifurcations with one- or highdimensional internal dynamics."
author:
- first_name: Sören
full_name: Schwenker, Sören
id: '97359'
last_name: Schwenker
orcid: 0000-0002-8054-2058
citation:
ama: Schwenker S. Genericity in Network Dynamics. Universität Hamburg; 2019.
apa: Schwenker, S. (2019). Genericity in Network Dynamics. Universität Hamburg.
bibtex: '@book{Schwenker_2019, place={Hamburg}, title={Genericity in Network Dynamics},
publisher={Universität Hamburg}, author={Schwenker, Sören}, year={2019} }'
chicago: 'Schwenker, Sören. Genericity in Network Dynamics. Hamburg: Universität
Hamburg, 2019.'
ieee: 'S. Schwenker, Genericity in Network Dynamics. Hamburg: Universität
Hamburg, 2019.'
mla: Schwenker, Sören. Genericity in Network Dynamics. Universität Hamburg,
2019.
short: S. Schwenker, Genericity in Network Dynamics, Universität Hamburg, Hamburg,
2019.
date_created: 2022-09-06T11:41:13Z
date_updated: 2022-09-07T08:32:14Z
extern: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ediss.sub.uni-hamburg.de/handle/ediss/6159
oa: '1'
place: Hamburg
publisher: Universität Hamburg
status: public
supervisor:
- first_name: Reiner
full_name: Lauterbach, Reiner
last_name: Lauterbach
title: Genericity in Network Dynamics
type: dissertation
user_id: '97359'
year: '2019'
...
---
_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. Numerische Mathematik. 2019;143(4):797-853.
doi:10.1007/s00211-019-01074-2
apa: Kovács, B., Li, B., & Lubich, C. (2019). A convergent evolving finite element
algorithm for mean curvature flow of closed surfaces. Numerische Mathematik,
143(4), 797–853. https://doi.org/10.1007/s00211-019-01074-2
bibtex: '@article{Kovács_Li_Lubich_2019, title={A convergent evolving finite element
algorithm for mean curvature flow of closed surfaces}, volume={143}, DOI={10.1007/s00211-019-01074-2},
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.” Numerische
Mathematik 143, no. 4 (2019): 797–853. https://doi.org/10.1007/s00211-019-01074-2.'
ieee: 'B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm
for mean curvature flow of closed surfaces,” Numerische Mathematik, vol.
143, no. 4, pp. 797–853, 2019, doi: 10.1007/s00211-019-01074-2.'
mla: Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for
Mean Curvature Flow of Closed Surfaces.” Numerische Mathematik, vol. 143,
no. 4, Springer Science and Business Media LLC, 2019, pp. 797–853, doi:10.1007/s00211-019-01074-2.
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'
...