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Multilevel correction adaptive finite element method for semilinear elliptic equation

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Abstract

A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary value problem. The convergence and optimal complexity of the new scheme can be derived theoretically and demonstrated numerically.

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Author information

Authors and Affiliations

  1. LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences No. 55, Zhongguancun Donglu, Beijing, 100190, China

    Qun Lin, Hehu Xie & Fei Xu

Authors
  1. Qun Lin
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  2. Hehu Xie
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  3. Fei Xu
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Corresponding author

Correspondence to Qun Lin.

Additional information

Cordially dedicated to Prof. Ivo Babuška on the occasion of his 90th birthday

This work was supported in part by National Science Foundations of China (NSFC 91330202, 11371026, 11001259, 11031006, 2011CB309703) and the National Center for Mathematics and Interdisciplinary Science.

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Lin, Q., Xie, H. & Xu, F. Multilevel correction adaptive finite element method for semilinear elliptic equation. Appl Math 60, 527–550 (2015). https://doi.org/10.1007/s10492-015-0110-x

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  • DOI: https://doi.org/10.1007/s10492-015-0110-x

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