MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 163-179 (2002)

On discontinuous Galerkin methods for
nonlinear convection-diffusion problems
and compressible flow

V. Dolejsi, M. Feistauer, C. Schwab

V. Dolejsi, M. Feistauer, Faculty of Mathematics and Physics, Charles University Prague, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail:,
C. Schwab, Seminar for Applied Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland, e-mail:

Abstract: The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.

Keywords: discontinuous Galerkin finite element method, numerical flux, conservation laws, convection-diffusion problems, limiting of order of accuracy, numerical solution of compressible Euler equations

Classification (MSC2000): 65M15, 76M10, 76M12

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