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CONVERGENCE OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR HYPERBOLIC CONSERVATION LAWS
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1995
Year
Numerical AnalysisFinite Element MethodEntropy InequalitiesEngineeringScalar Conservation LawsHyperbolic Conservation LawNumerical SimulationConservation LawsNonlinear Hyperbolic ProblemHyperbolic EquationComputational MechanicsBoundary Element MethodNumerical Method For Partial Differential EquationMultiscale Modeling
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.