On some aspects of the discontinuous Galerkin finite element method for conservation laws

Authors:
Vít Dolejší;Miloslav Feistauer;Christoph Schwab
Affiliations:
Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 18600 Praha 8, Czech Republic;Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 18600 Praha 8, Czech Republic;Seminar of Applied Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland
Venue:
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Year:
2003

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Abstract

The paper is concerned with the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin (FVDG) method, which is a generalization of the combined finite volume-finite element (FV-FE) method. Its advantage is the use of only one mesh (in contrast to the combined FV-FE schemes). However, it is of the first order only. (b) Further, the pure DGFE method of higher order is considered. In this case, a new limiting is developed to avoid spurious oscillations in the vicinity of shocks.