Abstract
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.
Original language | English (US) |
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Pages (from-to) | 264-285 |
Number of pages | 22 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 39 |
Issue number | 1 |
DOIs | |
State | Published - 2002 |
Keywords
- Cartesian grids
- Discontinuous Galerkin methods
- Elliptic problems
- Finite elements
- Superconvergence