Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations

2013/11/27 by Waixiang, Cao, Zhimin, Zhang, Qingsong, Zou · 2 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1311.6938

Abstract

In this paper, we study superconvergence properties of the discontinuous Galerkin (DG) method for one-dimensional linear hyperbolic equation when upwind fluxes are used. We prove, for any polynomial degree k, the 2k+1th (or 2k+1/2th) superconvergence rate of the DG approximation at the downwind points and for the domain average under quasi-uniform meshes and some suitable initial discretization. Moreover, we prove that the derivative approximation of the DG solution is superconvergent with a rate k+1 at all interior left Radau points. All theoretical finding are confirmed by numerical experiments.

Cited by

• On the Superconvergence of ESFR Schemes
• On the Stability Barrier of Hermite Type Discretizations of Advection Equations

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