Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations

Waixiang Cao; Zhimin Zhang

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arXiv · 1401.5150

Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations

Waixiang Cao·Zhimin Zhang

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Abstract

In this paper, we study superconvergence properties of the local discontinuous Galerkin method for one-dimensional linear parabolic equations when alternating fluxes are used. We prove, for any polynomial degree $k$, that the numerical fluxes converge at a rate of $2k+1$ (or $2k+1/2$) for all mesh nodes and the domain average under some suitable initial discretization. We further prove a $k+1$th superconvergence rate for the derivative approximation and a $k+2$th superconvergence rate for the function value approximation at the Radau points. Numerical experiments demonstrate that in most cases, our error estimates are optimal, i.e., the error bounds are sharp.

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BibTeX RIS

Waixiang Cao, Zhimin Zhang. 2014-01-21. Superconvergence of Local Discontinuous Galerkin method for one-dimensional linear parabolic equations. https://arxiv.org/abs/1401.5150

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