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High-precision computation of the weak Galerkin methods for the fourth-order problem

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Abstract

The weak Galerkin form of the finite element method, requiring only C0 basis function, is applied to the biharmonic equation. The computational procedure is thoroughly considered. Local orthogonal bases on triangulations are constructed using various sets of interpolation points with the Gram-Schmidt or Levenberg-Marquardt methods. Comparison and high-precision computations are carried out, and convergence rates are provided up to degree 11 for L2, 10 for H1, and 9 for H2, suggesting that the algorithm is useful for a variety of computations.

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Funding

John Burkardt was supported in part by the US Air Force Office of Scientific Research grant FA9550-15-1-0001. Max Gunzburger was supported in part by the US Air Force Office of Scientific Research grant FA9550-15-1-0001. Wenju Zhao was supported in part by the US Air Force Office of Scientific Research grant FA9550-15-1-0001.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    John Burkardt

  2. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32304, USA

    Max Gunzburger & Wenju Zhao

  3. Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, China

    Wenju Zhao

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  1. John Burkardt
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  2. Max Gunzburger
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  3. Wenju Zhao
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Correspondence to Wenju Zhao.

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Burkardt, J., Gunzburger, M. & Zhao, W. High-precision computation of the weak Galerkin methods for the fourth-order problem. Numer Algor 84, 181–205 (2020). https://doi.org/10.1007/s11075-019-00751-5

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  • DOI: https://doi.org/10.1007/s11075-019-00751-5

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