Abstract
In this manuscript we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of scalar first-order hyperbolic partial differential problems on triangular meshes. We explicitly write the basis functions for the error spaces corresponding to several finite element spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem. We also show global superconvergence for discontinuous solutions on triangular meshes. The a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement for smooth and discontinuous solutions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 15-49 |
| Number of pages | 35 |
| Journal | Journal of Scientific Computing |
| Volume | 38 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2009 |
| Externally published | Yes |
Keywords
- A posteriori error estimation
- Discontinuous Galerkin method
- Hyperbolic problems
- Superconvergence
ASJC Scopus subject areas
- Software
- Theoretical Computer Science
- Numerical Analysis
- Engineering(all)
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics