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A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  18 January 2017

Zhongguo Zhou  and
Dong Liang
Zhongguo Zhou*
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China School of Information Science and Engineering, Shandong Agricultural University, Taian, Shandong 271018, China
Dong Liang*
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
*
*Corresponding author. Email:zhouzhongguo@mail.sdu.edu.cn (Z. G. Zhou), dliang@mathstat.yorku.ca (D. Liang)
*Corresponding author. Email:zhouzhongguo@mail.sdu.edu.cn (Z. G. Zhou), dliang@mathstat.yorku.ca (D. Liang)
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Abstract

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.

Keywords

Diffusion equationstime second-ordermass-conservedimplicit-explicit domain decompositioninterface fluxes

MSC classification

Secondary: 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 65M55: Multigrid methods; domain decomposition 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 795 - 817
Copyright
Copyright © Global-Science Press 2017 

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