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A computational study of the weak Galerkin method for second-order elliptic equations

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Abstract

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye (2011) for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established in Wang and Ye (2011). The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.

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Authors and Affiliations

  1. Department of Applied Science, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Lin Mu

  2. Division of Mathematical Sciences, National Science Foundation, Arlington, VA, 22230, USA

    Junping Wang

  3. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, USA

    Yanqiu Wang

  4. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Xiu Ye

Authors
  1. Lin Mu
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  2. Junping Wang
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  3. Yanqiu Wang
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  4. Xiu Ye
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Corresponding author

Correspondence to Xiu Ye.

Additional information

The research of J. Wang was supported by the NSF IR/D program, while working at the National Science Foundation. However, any opinion, finding, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

The research of X. Ye was supported in part by the National Science Foundation under Grant No. DMS-1115097.

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Mu, L., Wang, J., Wang, Y. et al. A computational study of the weak Galerkin method for second-order elliptic equations. Numer Algor 63, 753–777 (2013). https://doi.org/10.1007/s11075-012-9651-1

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  • DOI: https://doi.org/10.1007/s11075-012-9651-1

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