The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations (Communications in Computational Physics, 2018)
In the paper, we develop and analyze a new mass-preserving splitting domaindecomposition method over multiple sub-domains for solving parabolic equations.The domain is divided into non-overlapping multi-bock sub-domains. On theinterfaces 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 computedby the splitting one-dimensional implicit solution-flux coupled scheme. Theimportant feature is that the proposed scheme is mass conservative over multiple non-overlappingsub-domains. Analyzing the mass-preserving S-DDM scheme is difficultover non-overlapping multi-block sub-domains due to the combination of the splittingtechnique and the domain decomposition at each time step. We prove theoreticallythat our scheme satisfies conservation of mass over multi-block non-overlapping sub-domainsand it is unconditionally stable. We further prove the convergence and obtainthe error estimate in $L^2$-norm. Numerical experiments confirm theoretical results.