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Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems

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Abstract

In this paper, some local and parallel discretizations and adaptive finite element algorithms are proposed and analyzed for nonlinear elliptic boundary value problems in both two and three dimensions. The main technique is to use a standard finite element discretization on a coarse grid to approximate low frequencies and then to apply some linearized discretization on a fine grid to correct the resulted residual (which contains mostly high frequencies) by some local/parallel procedures. The theoretical tools for analyzing these methods are some local a priori and a posteriori error estimates for finite element solutions on general shape-regular grids that are also obtained in this paper.

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Authors and Affiliations

  1. Center for Computational Mathematics and Applications and Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Jinchao Xu

  2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, China

    Aihui Zhou

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  1. Jinchao Xu
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Xu, J., Zhou, A. Local and Parallel Finite Element Algorithms Based on Two-Grid Discretizations for Nonlinear Problems. Advances in Computational Mathematics 14, 293–327 (2001). https://doi.org/10.1023/A:1012284322811

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