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Correlation between the discontinuous Galerkin method and MUSCL-type schemes

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Abstract

The discontinuous Galerkin method is compared with MUSCL-type schemes. The description and the analysis of the schemes are presented by using the solution of the linear advection equation as an example. The techniques for a generalization of these schemes to the case of solving nonlinear and multidimensional problems are considered. The correlation between the discontinuous Galerkin method and MUSCL-type schemes, as well as their distinctive features, are revealed. The criteria of the accuracy and the efficiency of the schemes as applied to problems of various classes are discussed.

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Authors and Affiliations

  1. Russian Federal Nuclear Center (All-Russian Research Institute of Experimental Physics), pr. Mira 37, Sarov, Nizhny Novgorod oblast, 607188, Russia

    A. V. Rodionov

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Original Russian Text © A.V. Rodionov, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 10, pp. 96–116.

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Rodionov, A.V. Correlation between the discontinuous Galerkin method and MUSCL-type schemes. Math Models Comput Simul 8, 285–300 (2016). https://doi.org/10.1134/S207004821603008X

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  • DOI: https://doi.org/10.1134/S207004821603008X

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