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

Eskil Hansen and Erik Henningsson

10.4208/cicp.scpde14.22s

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

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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.

  • History

Published online: 2018-04

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