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A discontinuous Galerkin recovery scheme with stabilization for diffusion problems

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Abstract

In this work, ideas previously introduced for a discontinuous Galerkin recovery method in one dimension, that involves a penalty stabilization term, are extended to an elliptic differential equation in several dimensions and different types of boundary conditions and meshes. Using standard arguments for other existing discontinuous Galerkin methods, we show results of existence and uniqueness of the solution. Also, optimal convergence rates are proved theoretically and confirmed numerically. Likewise, the numerical experiments allow us to analyze of the effect of the stabilization parameter.

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Acknowledgements

The authors want to thank the Universidad Nacional de Colombia, for the support for this project. We also want to thank the reviewers for their valuable suggestions that improved this paper, in a considerable way.

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  1. Escuela de Matemáticas, Universidad Nacional de Colombia, Sede Medellín, Colombia

    Mauricio Osorio & Wilmar Imbachí

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  1. Mauricio Osorio
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  2. Wilmar Imbachí
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Correspondence to Mauricio Osorio.

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Osorio, M., Imbachí, W. A discontinuous Galerkin recovery scheme with stabilization for diffusion problems. Calcolo 57, 33 (2020). https://doi.org/10.1007/s10092-020-00384-4

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  • DOI: https://doi.org/10.1007/s10092-020-00384-4

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