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Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations

Eisenmann, Monika and Hansen, Eskil LU (2018) In Numerische Mathematik 140(4). p.913-938
Abstract

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the p-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting... (More)

Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the p-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approximation theory for nonlinear semigroups.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Domain decomposition, Time integration, Operator splitting, Convergence analysis, Degenerate parabolic equations
in
Numerische Mathematik
volume
140
issue
4
pages
913 - 938
publisher
Springer
external identifiers
  • scopus:85049574782
ISSN
0029-599X
DOI
10.1007/s00211-018-0985-z
language
English
LU publication?
yes
id
941ffc4d-af18-4ae2-b2a9-dd29045151a8
alternative location
https://arxiv.org/abs/1708.01479
date added to LUP
2018-07-20 12:04:07
date last changed
2019-01-19 03:00:09
@article{941ffc4d-af18-4ae2-b2a9-dd29045151a8,
  abstract     = {<p>Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the p-Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approximation theory for nonlinear semigroups.</p>},
  author       = {Eisenmann, Monika and Hansen, Eskil},
  issn         = {0029-599X},
  keyword      = {Domain decomposition,Time integration,Operator splitting,Convergence analysis,Degenerate parabolic equations},
  language     = {eng},
  number       = {4},
  pages        = {913--938},
  publisher    = {Springer},
  series       = {Numerische Mathematik},
  title        = {Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations},
  url          = {http://dx.doi.org/10.1007/s00211-018-0985-z},
  volume       = {140},
  year         = {2018},
}