A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations
(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:
https://lup.lub.lu.se/record/c1e9aa1b-1a1c-448e-85dc-f2c161c2bcec
- author
- Hansen, Eskil LU and Henningsson, Erik LU
- organization
- publishing date
- 2016-05
- 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
- wos:000376456600010
- 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
- 2024-03-06 22:47:26
@article{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}}, keywords = {{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 = {{Global Science Press}}, 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}}, doi = {{10.4208/cicp.scpde14.22s}}, volume = {{19}}, year = {{2016}}, }