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Discontinuous Galerkin methods for fractional elliptic problems

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Abstract

The aim of this paper is to provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann–Liouville fractional elliptic problems on a finite domain. The boundedness and stability analysis of the primal bilinear form are provided. A priori error estimate under energy norm and optimal error estimate under \(L^{2}\) norm are obtained for DG methods of the different formulations. Finally, the performed numerical examples confirm the optimal convergence order of the different formulations.

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Acknowledgements

We thank the reviewers for their excellent comments and suggestions to revise and enhance portions of this paper. The author is also very much grateful to Editor-in-Chief (Prof. José E. Souza de Cursi) and Associate Editor (Prof. José A. Tenreiro Machado) for their pursuance.

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Unaizah, Qassim University, Qassim, Kingdom of Saudi Arabia

    Tarek Aboelenen

  2. Department of Mathematics, Assiut University, Assiut, 71516, Egypt

    Tarek Aboelenen

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  1. Tarek Aboelenen
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Correspondence to Tarek Aboelenen.

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Communicated by José Tenreiro Machado.

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Aboelenen, T. Discontinuous Galerkin methods for fractional elliptic problems. Comp. Appl. Math. 39, 88 (2020). https://doi.org/10.1007/s40314-020-1117-9

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