P. Castillo et al., An a priori error analysis of the local discontinuous Galerkin method for elliptic problems, SIAM J NUM, 38(5), 2000, pp. 1676-1706
In this paper, we present the rst a priori error analysis for the local dis
continuous Galerkin (LDG) method for a model elliptic problem. For arbitrar
y meshes with hanging nodes and elements of various shapes, we show that, f
or 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, whe
n polynomials of total degree at least k are used; if stabilization paramet
ers of order h(-1) are taken, the order of convergence of the potential inc
reases to k + 1. The optimality of these theoretical results is tested in a
series of numerical experiments on two dimensional domains.