1995•Mathematical Models and Methods in Applied SciencesRequires access

CONVERGENCE OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC CONSERVATION LAWS

Jérôme Jaffré, Claes Johnson, Anders Szepessy

Abstract

We prove convergence of the discontinuous Galerkin finite element method with polynomials of arbitrary degree q≥0 on general unstructured meshes for scalar conservation laws in multidimensions. We also prove for systems of conservation laws that limits of discontinuous Galerkin finite element solutions satisfy the entropy inequalities of the system related to convex entropies.

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Key concepts: Conservation law, Discontinuous Galerkin method, Mathematics, Finite element method, Polygon mesh, Applied mathematics, Convergence (economics), Entropy (arrow of time)