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Istituto di Matematica Applicata e Tecnologie Informatiche     
Castillo P., Cockburn B., Perugia I., Schoetzau D. An a priori error analysis of the Local Discontinuous Galerkin method for elliptic problems. Technical report ercim.cnr.ian//2000-1177, 2000.
 
 
Abstract
(English)
In this paper, we present the first a priori error analysis for the Local Discontinuous Galerkin method for a model elliptic problem. For arbitrary meshes with hanging nodes and elements of various shapes, we show that, for stabilization parameters of order one, the L$^2$-norm of the gradient and the L$^2$-norm of the potential are of order $k$ and $k+1/2$, respectively, when polynomials of total degree at least $k$ are used; if stabilization parameters of order $h^{-1}$ are taken, the order of convergence of the potential increases to $k+1$. The optimality of these theoretical results are tested in a series of numerical experiments on two dimensional domains. (SIAM J. Numer. Anal., 38 (2000), 1676-1706)
Subject Finite elements, discontinuous Galerkin methods, elliptic problems
65N30


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