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Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods

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Abstract

In this paper, we investigate a scheme for nonlinear reaction-diffusion equations using the mixed finite element methods. To linearize the mixed method equations, we use the two-grid algorithm. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy \(H=\mathcal{O}(h^{\frac{1}{2}})\). As a result, solving such a large class of nonlinear equations will not much more difficult than the solution of one linearized equation.

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Authors and Affiliations

  1. School of Mathematical and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, Guangdong, P.R. China

    Luoping Chen

  2. School of Mathematical Science, South China Normal University, Guangzhou, 520631, Guangdong, P.R. China

    Yanping Chen

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  1. Luoping Chen
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  2. Yanping Chen
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Correspondence to Yanping Chen.

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Chen, L., Chen, Y. Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods. J Sci Comput 49, 383–401 (2011). https://doi.org/10.1007/s10915-011-9469-3

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  • DOI: https://doi.org/10.1007/s10915-011-9469-3

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