V. Dolejsi, M. Feistauer, Faculty of Mathematics and Physics, Charles University Prague, Sokolovska 83, 186 75 Praha 8, Czech Republic, e-mail: dolejsi@karlin.mff.cuni.cz, feist@karlin.mff.cuni.cz; C. Schwab, Seminar for Applied Mathematics, ETH Zurich, Raemistrasse 101, CH-8092 Zurich, Switzerland, e-mail: schwab@math.ethz.ch
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 (MSC 2000): 65M15, 76M10, 76M12
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