Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids

Authors:
Bernardo Cockburn;Guido Kanschat;Ilaria Perugia;Dominik Schötzau
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2001

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Abstract

In this paper, we present a superconvergence result for the local discontinuous Galerkin (LDG) method for a model elliptic problem on Cartesian grids. We identify a special numerical flux for which the L2-norm of the gradient and the L2-norm of the potential are of orders k+1/2 and k+1, respectively, when tensor product polynomials of degree at most k are used; for arbitrary meshes, this special LDG method gives only the orders of convergence of k and k+1/2, respectively. We present a series of numerical examples which establish the sharpness of our theoretical results.