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A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  30 July 2015

Xingding Chen  and
Guangwei Yuan
Xingding Chen*
Affiliation:
Department of Mathematics, School of Science, Beijing Technology and Business University, Beijing 100048, P.R. China
Guangwei Yuan
Affiliation:
LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P.R. China
*
*Corresponding author. Email addresses: [email protected] (X. D. Chen), [email protected] (G. W. Yuan)
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Abstract

In this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

Keywords

Discrete maximum principlediscontinuous coefficientsdomain decompositionconstrained finite element method

MSC classification

Secondary: 65N12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 2 , August 2015 , pp. 297 - 320
Copyright
Copyright © Global-Science Press 2015 

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