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An analysis of the discontinuous Galerkin method for wave propagation problems. (English) Zbl 0933.65113
Summary: The dispersion and dissipation properties of the discontinuous Galerkin method are investigated with a view to simulating wave propagation phenomena. These properties are analyzed in the semidiscrete context of the one-dimensional scalar advection equation and the two-dimensional wave equation, discretized on triangular and quadrilateral elements. They are verified by the results from full numerical solutions of the simple scalar advection equation and the Euler equations. \(\copyright\) Academic Press.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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