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A cascadic multigrid method for a kind of semilinear elliptic problem

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Abstract

In this paper, we analyze a cascadic multigrid method for semilinear elliptic problems in which the derivative of the semilinear term is Hölder continuous. We first investigate the standard finite element error estimates of this kind of problem. We then solve the corresponding discrete problems using the cascadic multigrid method. We prove that the algorithm has an optimal order of convergence in energy norm and quasi-optimal computational complexity. We also report some numerical results to support the theory.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, Hunan, China

    Haixiong Yu

  2. College of Computer, Dongguan University of Technology, Dongguan, 523000, Guangdong, China

    Jinping Zeng

Authors
  1. Haixiong Yu
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  2. Jinping Zeng
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Correspondence to Haixiong Yu.

Additional information

The work was supported by the National Nature Science Foundation of P.R. China (Grant no. 10971058).

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Yu, H., Zeng, J. A cascadic multigrid method for a kind of semilinear elliptic problem. Numer Algor 58, 143–162 (2011). https://doi.org/10.1007/s11075-011-9450-0

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  • DOI: https://doi.org/10.1007/s11075-011-9450-0

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