Mass-preserving time second-order explicit–implicit domain decomposition schemes for solving parabolic equations with variable coefficients

Abstract

In this paper, the new mass-preserving time second-order explicit–implicit domain decomposition (DD) schemes for solving parabolic equations with various coefficients are proposed. In the schemes, first, the interface values on the interfaces of sub-domains are explicitly calculated, in which two kinds of explicit difference schemes are used. Second, the interior values in sub-domains are determined by the implicit schemes. Third, the interface values are recalculated explicitly to preserve mass. The important feature is that the developed schemes are more than first order in time step and the correction operators at the third step ensure the schemes’ mass conservative. The stability and convergence are analyzed for the two schemes. The optimal error estimates are obtained in the $H^1$ semi-norm under a stability condition. Numerical experiments confirm the theoretical results.