A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations
Year: 2016
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.scpde14.22s
Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1302–1316
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15