In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h 2 )-order superconvergence error estimate is established under the conditions of almost uniform
Superconvergence and H(div) projection for discontinuous Galerkin methods
✍ Scribed by Peter Bastian; Béatrice Rivière
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 494 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0271-2091
- DOI
- 10.1002/fld.562
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📜 SIMILAR VOLUMES
This paper presents a theoretical and numerical study of a class of discontinuous Galerkin methods that shows the approximation of the gradient superconverges at the zeros of the Legendre polynomials on a model 1D elliptic problem. Numerical experiments validate the theoretical results.
## Abstract In this paper, we review the development of local discontinuous Galerkin methods for elliptic problems. We explain the derivation of these methods and present the corresponding error estimates; we also mention how to couple them with standard conforming finite element methods. Numerical