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

Part of: Numerical analysis in abstract spaces Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 May 2016

Eskil Hansen  and
Erik Henningsson
Eskil Hansen*
Affiliation:
Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
Erik Henningsson*
Affiliation:
Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
*
*Corresponding author. Email addresses:eskil@maths.lth.se (E. Hansen), erikh@maths.lth.se (E. Henningsson)
*Corresponding author. Email addresses:eskil@maths.lth.se (E. Hansen), erikh@maths.lth.se (E. Henningsson)
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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.

Keywords

Douglas/Peaceman-Rachford schemesfull space-time discretizationdimension splittingconvergence orderevolution equationsfinite element methods

MSC classification

Secondary: 65J08: Abstract evolution equations 65M12: Stability and convergence of numerical methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1302 - 1316
Copyright
Copyright © Global-Science Press 2016 

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