A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations

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

Keywords: