A Full Space-Time Convergence Order Analysis of Operator Splittings for Linear Dissipative Evolution Equations. (17th May 2016)

• Record Type: Journal Article
• Authors: Hansen, Eskil; Henningsson, Erik
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1302
• Page End: 1316
• Publication Date: 2016-05-17
• Subjects: 65J08, -- 65M12, -- 65M60; Douglas/Peaceman-Rachford schemes, -- full space-time discretization, -- dimension splitting, -- convergence order, -- evolution equations, -- finite element methods; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.22s
• Languages: English
• ISSNs: 1815-2406

Abstract

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.