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A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations

Hansen, Eskil LU and Henningsson, Erik LU (2016) In Communications in Computational Physics 19(5). p.1302-1316
Abstract
The Douglas-Rachford and Peaceman-Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract results to dimension splitting of a 2D diffusion problem, where a finite element method is used for spatial discretization. To conclude, the convergence results are illustrated with numerical experiments.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Douglas/Peaceman-Rachford schemes, full space-time discretization, dimension splitting, convergence order, evolution equations, finite element methods
in
Communications in Computational Physics
volume
19
issue
5
pages
15 pages
publisher
Global Science Press
external identifiers
  • Scopus:84969234317
ISSN
1815-2406
DOI
10.4208/cicp.scpde14.22s
language
English
LU publication?
yes
id
c1e9aa1b-1a1c-448e-85dc-f2c161c2bcec
date added to LUP
2016-05-09 11:29:45
date last changed
2016-10-13 05:08:22
@misc{c1e9aa1b-1a1c-448e-85dc-f2c161c2bcec,
  abstract     = {The Douglas-Rachford and Peaceman-Rachford splitting methods are common choices for temporal discretizations of evolution equations. In this paper we combine these methods with spatial discretizations fulfilling some easily verifiable criteria. In the setting of linear dissipative evolution equations we prove optimal convergence orders, simultaneously in time and space. We apply our abstract results to dimension splitting of a 2D diffusion problem, where a finite element method is used for spatial discretization. To conclude, the convergence results are illustrated with numerical experiments.},
  author       = {Hansen, Eskil and Henningsson, Erik},
  issn         = {1815-2406},
  keyword      = {Douglas/Peaceman-Rachford schemes,full space-time discretization,dimension splitting,convergence order,evolution equations,finite element methods},
  language     = {eng},
  number       = {5},
  pages        = {1302--1316},
  publisher    = {ARRAY(0xa3ddc28)},
  series       = {Communications in Computational Physics},
  title        = {A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations},
  url          = {http://dx.doi.org/10.4208/cicp.scpde14.22s},
  volume       = {19},
  year         = {2016},
}