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

Hansen, Eskil LU and Eisenmann, Monika (2017)
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 general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. 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... (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 general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
submitted
subject
keywords
Domain decomposition, Time integration, Operator splitting, Convergence analysis, Degenerate parabolic equations
pages
21 pages
language
English
LU publication?
yes
id
727d5eec-e168-4154-96a1-63fb8146e4fd
alternative location
https://arxiv.org/abs/1708.01479
date added to LUP
2017-08-07 10:03:23
date last changed
2018-01-18 14:32:13
@misc{727d5eec-e168-4154-96a1-63fb8146e4fd,
  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 general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. 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.},
  author       = {Hansen, Eskil and Eisenmann, Monika},
  keyword      = {Domain decomposition,Time integration,Operator splitting,Convergence analysis,Degenerate parabolic equations},
  language     = {eng},
  note         = {Working Paper},
  pages        = {21},
  title        = {Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations},
  year         = {2017},
}