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arXiv · 1311.6938

Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations

Cao Waixiang·Zhang Zhimin·Zou Qingsong
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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 $2k+1$th (or $2k+1/2$th) 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.

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Cao Waixiang, Zhang Zhimin, Zou Qingsong. 2013-11-27. Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations. https://arxiv.org/abs/1311.6938

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