@Article{CiCP-19-2,
author = {},
title = {The Mass-Preserving S-DDM Scheme for Two-Dimensional Parabolic Equations},
journal = {Communications in Computational Physics},
year = {2016},
volume = {19},
number = {2},
pages = {411--441},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.070814.190615a},
url = {https://global-sci.com/article/80260/the-mass-preserving-s-ddm-scheme-for-two-dimensional-parabolic-equations}
}