TY - JOUR
T1 - An a priori error analysis of the local discontinuous Galerkin method for elliptic problems
AU - Castillo, Paul
AU - Cockburn, Bernardo
AU - Perugia, Ilaria
AU - Schötzau, Dominik
PY - 2001
Y1 - 2001
N2 - In this paper, we present the first a priori error analysis for the local discontinuous Galerkin (LDG) 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 L2-norm of the gradient and the L2-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 is tested in a series of numerical experiments on two dimensional domains.
AB - In this paper, we present the first a priori error analysis for the local discontinuous Galerkin (LDG) 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 L2-norm of the gradient and the L2-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 is tested in a series of numerical experiments on two dimensional domains.
KW - Discontinuous Galerkin methods
KW - Elliptic problems
KW - Finite elements
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U2 - 10.1137/S0036142900371003
DO - 10.1137/S0036142900371003
M3 - Article
AN - SCOPUS:0034548629
SN - 0036-1429
VL - 38
SP - 1676
EP - 1706
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 5
ER -