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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems
Hochbruck, Marlis | Köhler, JonasNumerische Mathematik, Vol. 150 (2022), Iss. 3 P.893
https://doi.org/10.1007/s00211-021-01262-z [Citations: 6] -
Additive domain decomposition operator splittings—convergence analyses in a dissipative framework
Hansen, Eskil | Henningsson, ErikIMA Journal of Numerical Analysis, Vol. (2016), Iss. P.drw043
https://doi.org/10.1093/imanum/drw043 [Citations: 1]