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A Rectangular Finite Volume Element Method for a Semilinear Elliptic Equation

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Abstract

In this paper we extend the idea of interpolated coefficients for semilinear problems to the finite volume element method based on rectangular partition. At first we introduce bilinear finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. Next we derive convergence estimate in H 1-norm and superconvergence of derivative. Finally an example is given to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Zhiguang Xiong & Yanping Chen

  2. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, People’s Republic of China

    Zhiguang Xiong

Authors
  1. Zhiguang Xiong
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  2. Yanping Chen
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Corresponding author

Correspondence to Yanping Chen.

Additional information

This work is supported by Program for New Century Excellent Talents in University of China State Education Ministry, National Science Foundation of China, the National Basic Research Program under the Grant (2005CB321703), the key project of China State Education Ministry (204098), Scientific Research Fund of Hunan Provincial Education Department, China Postdoctoral Science Foundation (No. 20060390894) and China Postdoctoral Science Foundation (No. 20060390894).

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Xiong, Z., Chen, Y. A Rectangular Finite Volume Element Method for a Semilinear Elliptic Equation. J Sci Comput 36, 177–191 (2008). https://doi.org/10.1007/s10915-007-9184-2

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  • DOI: https://doi.org/10.1007/s10915-007-9184-2

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