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Two-Grid method for nonlinear parabolic equations by expanded mixed finite element methods

Authors

  • Yanping Chen,

    Corresponding author
    1. Department of Computational Mathematics, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, People's Republic of China
    • Department of Computational Mathematics, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, People's Republic of China
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  • Luoping Chen,

    1. Department of Computational Mathematics, School of Mathematical and computational science, Sun Yat-Sen University, Guangzhou 510275, Guangdong, People's Republic of China
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  • Xiaochun Zhang

    1. Department of Computational Mathematics, School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, People's Republic of China
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Abstract

In this article, we develop a two-grid algorithm for nonlinear reaction diffusion equation (with nonlinear compressibility coefficient) discretized by expanded mixed finite element method. The key point is to use two-grid scheme to linearize the nonlinear term in the equations. The main procedure of the algorithm is solving a small-scaled nonlinear equations on the coarse grid and dealing with a linearized system on the fine space using the Newton iteration with the coarse grid solution. Error estimation to the expanded mixed finite element solution is analyzed in detail. We also show that two-grid solution achieves the same accuracy as long as the mesh sizes satisfy H = O(h1/2). Two numerical experiments are given to verify the effectiveness of the algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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