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Superconvergence of Discontinuous Galerkin Methods for Elliptic Boundary Value Problems

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Abstract

In this paper, we present a unified analysis of the superconvergence property for a large class of mixed discontinuous Galerkin methods. This analysis applies to both the Poisson equation and linear elasticity problems with symmetric stress formulations. Based on this result, some locally postprocess schemes are employed to improve the accuracy of displacement by order \(\min (k+1, 2)\) if polynomials of degree k are employed for displacement. Some numerical experiments are carried out to validate the theoretical results.

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Acknowledgements

The author wishes to thank the partial support from the Center for Computational Mathematics and Applications, the Pennsylvania State University. The author would also like to thank Professor Jinchao Xu from the Pennsylvania State University and Professor Jun Hu from the Peking University for their guidance and helpful suggestions pertaining to this work.

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  1. Department of Mathematics, Pennsylvania State University, University Park, PA, State College, 16802, USA

    Limin Ma

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Correspondence to Limin Ma.

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The numerical examples are simulated on FEniCs. The model code that support the findings of this study are openly available at https://github.com/maliminmath/MaCodeOnline.

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The work of the author was partially supported by Center for Computational Mathematics and Applications, The Pennsylvania State University.

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Ma, L. Superconvergence of Discontinuous Galerkin Methods for Elliptic Boundary Value Problems . J Sci Comput 88, 62 (2021). https://doi.org/10.1007/s10915-021-01589-7

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  • DOI: https://doi.org/10.1007/s10915-021-01589-7

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