Abstract
We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.
Original language | English |
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Pages (from-to) | 57-69 |
Number of pages | 13 |
Journal | Computing and Visualization in Science |
Volume | 9 |
Issue number | 2 |
DOIs | |
State | Published - Jul 2006 |
Keywords
- Adaptive Gauss-Seidel iteration
- Compatibility condition
- Eikonal equation
- Hamilton-Jacobi equation
- Hopf-Lax formula
- Linear finite elements
- Local variational principle
- Viscosity solutions