2014/01/21 by Cao, Waixiang, Zhang, Zhimin
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1401.5150
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+1th superconvergence rate for the derivative approximation and a k+2th 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.