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

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, respecti...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2002, Vol.39 (1), p.264-285
Main Authors: Cockburn, Bernardo, Kanschat, Guido, Perugia, Ilaria, Schötzau, Dominik
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Boundary conditions
Cartesianism
Convergent boundaries
Degrees of polynomials
Error analysis
Estimation methods
Exact sciences and technology
Galerkin methods
Mathematical discontinuity
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Perceptron convergence procedure
Polynomials
Sciences and techniques of general use
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Summary: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.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142900371544