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A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems

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Abstract

In this paper we present a stabilized Discontinuous Galerkin (DG) method for hyperbolic and convection dominated problems. The presented scheme can be used in several space dimension and with a wide range of grid types. The stabilization method preserves the locality of the DG method and therefore allows to apply the same parallelization techniques used for the underlying DG method. As an example problem we consider the Euler equations of gas dynamics for an ideal gas. We demonstrate the stability and accuracy of our method through the detailed study of several test cases in two space dimension on both unstructured and cartesian grids. We show that our stabilization approach preserves the advantages of the DG method in regions where stabilization is not necessary. Furthermore, we give an outlook to adaptive and parallel calculations in 3d.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Andreas Dedner

  2. Applied Mathematics, University of Freiburg, Hermann-Herder-Strasse 10, 79104, Freiburg, Germany

    Robert Klöfkorn

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  1. Andreas Dedner
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  2. Robert Klöfkorn
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Correspondence to Robert Klöfkorn.

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Dedner, A., Klöfkorn, R. A Generic Stabilization Approach for Higher Order Discontinuous Galerkin Methods for Convection Dominated Problems. J Sci Comput 47, 365–388 (2011). https://doi.org/10.1007/s10915-010-9448-0

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  • DOI: https://doi.org/10.1007/s10915-010-9448-0

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