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arXiv · 1506.01859

On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws

Georg May·Mohammad Zakerzadeh
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Abstract

We prove convergence of a class of space-time discontinuous Galerkin schemes for scalar hyperbolic conservation laws. Convergence to the unique entropy solution is shown for all orders of polynomial approximation, provided strictly monotone flux functions and a suitable shock-capturing operator are used. The main improvement, compared to previously published results of similar scope, is that no streamline-diffusion stabilization is used. This is the way discontinuous Galerkin schemes were originally proposed, and are most often used in practice.

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Georg May, Mohammad Zakerzadeh. 2015-06-05. On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws. https://arxiv.org/abs/1506.01859

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