Abstract
We present a collection of theoretical results for characteristic Galerkin approximations of scalar hyperbolic conservation laws. With piecewise constant basis functions, the characteristic Galerkin method is unconditionally stable, monotone, TVD and L ∞-norm-nonincreasing in any space dimension, but it is only first order accurate. Two recovery procedures are investigated in order to improve the accuracy: continuous and discontinuous linear recovery. Upon mesh refinement, the characteristic Galerkin method with either of these recovery schemes converges to the entropy solution of the conservation law.KeywordsFinite Difference SchemeEntropy SolutionCourant NumberHyperbolic ProblemUltimate Conservative Difference SchemeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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