The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations. (1st February 2016)

• Record Type: Journal Article
• Authors: Zhou, Zhongguo; Liang, Dong
• Is Part Of: Communications in computational physics. Volume 19:Number 2(2016:Feb.)
• Page Start: 411
• Page End: 441
• Publication Date: 2016-02-01
• Subjects: 65M06, -- 65M12, -- 65M55, -- 76S05; Parabolic equations, -- S-DDM, -- mass-preserving, -- unconditional stability, -- convergence, -- multi-blocks, -- non-overlapping; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.070814.190615a
• Languages: English
• ISSNs: 1815-2406

Abstract

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 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 L 2 -norm. Numerical experiments confirm theoretical results.