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Adaptive Bilinear Element Finite Volume Methods for Second-Order Elliptic Problems on Nonmatching Grids

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Abstract

In this article, we propose and analyze two kinds of adaptive bilinear element finite volume methods for second-order elliptic problems on nonmatching grids. One of them chooses the piecewise bilinear finite element space as the trial function space, which is continuous on the matching part of a grid and is discontinuous on the nonmatching part of it. The other directly uses discontinuous piecewise bilinear element space for the trial function space. A priori estimations ensure the convergence and a posteriori estimations pave the way for adaptive methods. Several numerical experiments are presented to conform our theoretical results.

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Authors and Affiliations

  1. Institute of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Yanli Chen

  2. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Yonghai Li

  3. Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, People’s Republic of China

    Zhiqiang Sheng & Guangwei Yuan

Authors
  1. Yanli Chen
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  2. Yonghai Li
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  3. Zhiqiang Sheng
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  4. Guangwei Yuan
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Corresponding author

Correspondence to Yonghai Li.

Additional information

Supported by the ‘985’ program of Jilin University and the National Natural Science Foundation of China (Nos. 11371170 and 11171036).

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Chen, Y., Li, Y., Sheng, Z. et al. Adaptive Bilinear Element Finite Volume Methods for Second-Order Elliptic Problems on Nonmatching Grids. J Sci Comput 64, 130–150 (2015). https://doi.org/10.1007/s10915-014-9927-9

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  • DOI: https://doi.org/10.1007/s10915-014-9927-9

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