Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations
Numerical Analysis
2013-11-28 v1
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 , the th (or 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 at all interior left Radau points. All theoretical finding are confirmed by numerical experiments.
Cite
@article{arxiv.1311.6938,
title = {Superconvergence of Discontinuous Galerkin method for linear hyperbolic equations},
author = {Cao Waixiang and Zhang Zhimin and Zou Qingsong},
journal= {arXiv preprint arXiv:1311.6938},
year = {2013}
}