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A variational approach to the sum splitting scheme

Eisenmann, Monika LU orcid and Hansen, Eskil LU (2022) In IMA Journal of Numerical Analysis 42(1). p.923-950
Abstract
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we present a sum splitting scheme that comes with a straightforward parallelization strategy. The convergence analysis is carried out in a variational framework that allows for a general setting and, in particular, nontrivial temporal coefficients. The aim of this work is to illustrate the significant advantages of a variational framework for operator splittings and to use this to extend semigroup-based theory for this type of scheme.


Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Nonlinear evolution problem, monotone operator, operator splitting, convergence
in
IMA Journal of Numerical Analysis
volume
42
issue
1
pages
923 - 950
publisher
Oxford University Press
ISSN
0272-4979
DOI
10.1093/imanum/draa100
project
Next generation numerical partitioning schemes for time dependent PDEs
language
English
LU publication?
yes
id
2f8cce91-4d80-48aa-83ab-820cbc6d3ed2
alternative location
http://arxiv.org/abs/1902.10023
date added to LUP
2019-02-27 09:56:17
date last changed
2022-03-24 12:43:01
@article{2f8cce91-4d80-48aa-83ab-820cbc6d3ed2,
  abstract     = {{Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we present a sum splitting scheme that comes with a straightforward parallelization strategy. The convergence analysis is carried out in a variational framework that allows for a general setting and, in particular, nontrivial temporal coefficients. The aim of this work is to illustrate the significant advantages of a variational framework for operator splittings and to use this to extend semigroup-based theory for this type of scheme.<br/><br/><br/>}},
  author       = {{Eisenmann, Monika and Hansen, Eskil}},
  issn         = {{0272-4979}},
  keywords     = {{Nonlinear evolution problem; monotone operator; operator splitting; convergence}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{1}},
  pages        = {{923--950}},
  publisher    = {{Oxford University Press}},
  series       = {{IMA Journal of Numerical Analysis}},
  title        = {{A variational approach to the sum splitting scheme}},
  url          = {{http://dx.doi.org/10.1093/imanum/draa100}},
  doi          = {{10.1093/imanum/draa100}},
  volume       = {{42}},
  year         = {{2022}},
}