Volume 19, Issue 5
A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations

Eskil Hansen & Erik Henningsson

Commun. Comput. Phys., 19 (2016), pp. 1302-1316.

Published online: 2018-04

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  • 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.

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@Article{CiCP-19-1302, author = {}, title = {A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.22s}, url = {http://global-sci.org/intro/article_detail/cicp/11130.html} }
TY - JOUR T1 - A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations JO - Communications in Computational Physics VL - 5 SP - 1302 EP - 1316 PY - 2018 DA - 2018/04 SN - 19 DO - http://dor.org/10.4208/cicp.scpde14.22s UR - https://global-sci.org/intro/article_detail/cicp/11130.html KW - AB -

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.

Eskil Hansen & Erik Henningsson. (2020). A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations. Communications in Computational Physics. 19 (5). 1302-1316. doi:10.4208/cicp.scpde14.22s
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