Abstract
In this paper we consider the numerical solution of first-order Hamilton-Jacobi equations using the combination of a discontinuous Galerkin finite element method and an adaptive $r$-refinement (mesh movement) strategy. Particular attention is given to the choice of an appropriate adaptivity criterion when the solution becomes discontinuous. Numerical examples in one and two dimensions are presented to demonstrate the effectiveness of the adaptive procedure.
| Original language | English |
|---|---|
| Pages (from-to) | 2258-2282 |
| Number of pages | 25 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 29 |
| Issue number | 6 |
| Early online date | 5 Oct 2007 |
| DOIs | |
| Publication status | Published - 2007 |
Keywords
- adaptivity
- moving meshes
- discontinuous Galerkin finite elements
- Hamlton-Jacobi equations