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The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

Part of: Flows in porous media; filtration; seepage Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  01 February 2016

Zhongguo Zhou  and
Dong Liang
Zhongguo Zhou
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong, 250100, China
Dong Liang*
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong, 250100, China Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J1P3, Canada
*
*Corresponding author. Email addresses:zhouzhongguo@mail.sdu.edu.cn (Z.Zhou), dliang@mathstat.yorku.ca (D. Liang)

Abstract

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In the paper, we develop and analyze a new mass-preserving splitting domain decomposition method over multiple sub-domains for solving parabolic equations. The domain is divided into non-overlapping multi-bock sub-domains. On the interfaces of sub-domains, the interface fluxes are computed by the semi-implicit (explicit) flux scheme. The solutions and fluxes in the interiors of sub-domains are computed by the splitting one-dimensional implicit solution-flux coupled scheme. The important feature is that the proposed scheme is mass conservative over multiple non-overlapping sub-domains. Analyzing the mass-preserving S-DDM scheme is difficult over non-overlapping multi-block sub-domains due to the combination of the splitting technique and the domain decomposition at each time step. We prove theoretically that our scheme satisfies conservation of mass over multi-block non-overlapping sub-domains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L2-norm. Numerical experiments confirm theoretical results.

Keywords

Parabolic equationsS-DDMmass-preservingunconditional stabilityconvergencemulti-blocksnon-overlapping

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 65M55: Multigrid methods; domain decomposition 76S05: Flows in porous media; filtration; seepage

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 411 - 441
Copyright
Copyright © Global-Science Press 2016 

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