Volume 19, Issue 2
The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations

Zhongguo Zhou and Dong Liang


Commun. Comput. Phys., 19 (2016), pp. 411-441.

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  • Abstract

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 nonoverlapping 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 subdomains and it is unconditionally stable. We further prove the convergence and obtain the error estimate in L 2 -norm. Numerical experiments confirm theoretical results.

  • History

Published online: 2018-04

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