标题：A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations
作者：Zhou, Zhongguo; Liang, Dong
作者机构：[Zhou, Zhongguo] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Zhou, Zhongguo] Shandong Agr Univ, Sch Informat Sci & Engn, Tai 更多
通讯作者地址：[Liang, D]York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada.
来源：ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
关键词：Diffusion equations; time second-order; mass-conserved;; implicit-explicit domain decomposition; interface fluxes
摘要：In the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor's expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable condition r <= 3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.