A variational approach to the sum splitting scheme
Eisenmann, Monika LU
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:
https://lup.lub.lu.se/record/2f8cce91-4d80-48aa-83ab-820cbc6d3ed2
- author
- Eisenmann, Monika
LU
and Hansen, Eskil
LU
- organization
- publishing date
- 2022-01-20
- 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
- external identifiers
-
- scopus:85133819649
- 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
- 2025-02-12 15:53:12
@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}},
}