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On optimal node and polynomial degree distribution in one-dimensional \(hp\)-FEM

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Abstract

We are concerned with the task of constructing an optimal higher-order finite element mesh under a constraint on the total number of degrees of freedom. The motivation for this work is to obtain a truly optimal higher-order finite element mesh that can be used to compare the quality of automatic adaptive algorithms. Minimized is the approximation error in a global norm. Optimization variables include the number of elements, positions of nodes, and polynomial degrees of elements. Optimization methods and software that we use are described, and numerical results are presented.

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Acknowledgments

The first author is grateful to Dr. Richard (Dick) Haas for many fruitful discussions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29 , Prague 6, Czech Republic

    Jan Chleboun

  2. Department of Mathematics and Statistics, University of Nevada, Reno, NV, 89557-0084, USA

    Pavel Solin

  3. Institute of Thermomechanics, Dolejskova 5, Prague, Czech Republic

    Pavel Solin

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  1. Jan Chleboun
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  2. Pavel Solin
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Correspondence to Jan Chleboun.

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The research of the first author was supported by Czech Science Foundation Grant No. P105/10/1682. The research of the second author was partly supported by Czech Science Foundation Grant No. P105/10/1682.

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Chleboun, J., Solin, P. On optimal node and polynomial degree distribution in one-dimensional \(hp\)-FEM. Computing 95 (Suppl 1), 75–88 (2013). https://doi.org/10.1007/s00607-012-0232-x

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  • DOI: https://doi.org/10.1007/s00607-012-0232-x

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