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.
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© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Morton, K.W., Süli, E., Lin, P. (1993). Characteristic Galerkin Methods for Hyperbolic Problems. In: Donato, A., Oliveri, F. (eds) Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Notes on Numerical Fluid Mechanics (NNFM), vol 43. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87871-7_52
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DOI: https://doi.org/10.1007/978-3-322-87871-7_52
Publisher Name: Vieweg+Teubner Verlag
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