Istituto di Matematica Applicata e Tecnologie Informatiche     
Cockburn B., Kanschat G., Perugia I., Schoetzau D. Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. Technical report ercim.cnr.ian//2000-1178, 2000.
In this paper, we present a super-convergence result for the local discontinuous Galerkin (LDG) method for a model elliptic problem on Cartesian grids. We identify a {em special} numerical flux for which the L$^2$-norm of the gradient and the L$^2$-norm of the potential are of order $k+1/2$ 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. (SIAM J. Numer. Anal., 39 (2001), 264-285)
Subject Finite elements, discontinuous Galerkin methods, super-convergence, elliptic problems, Cartesian grids.

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