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

2015/06/05 by May, Georg, Zakerzadeh, Mohammad
#FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1506.01859

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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