A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations (Advances in Applied Mathematics and Mechanics, 2018)
In the paper, a new time second-order mass-conserved implicit/explicit domaindecomposition method (DDM) for the diffusion equations is proposed. In thescheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutionsand fluxes at the previous time level, for which we apply high-order Taylor'sexpansion and transfer the time derivatives to spatial derivatives to improve the accuracy.Secondly, the interior solutions and fluxes in sub-domains are computed bythe implicit scheme and using the relations between solutions and fluxes, without anycorrection step. The mass conservation is proved and the convergence order of thenumerical solutions is proved to be second-order in both time and space steps. Thesuper-convergence of numerical fluxes is also proved to be second-order in both timeand space steps. The scheme is stable under the stable condition r≤3/5. The importantfeature is that the proposed domain decomposition scheme is mass-conserved and isof second order convergence in time. Numerical experiments confirm the theoreticalresults.