Abstract
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.
Original language | English (US) |
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Pages (from-to) | 1676-1706 |
Number of pages | 31 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 38 |
Issue number | 5 |
DOIs | |
State | Published - 2001 |
Keywords
- Discontinuous Galerkin methods
- Elliptic problems
- Finite elements