| 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. |
