Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains. (English) Zbl 0911.65091
Discretizations of Hamilton-Jacobi and level set equations on triangular grids are discussed. Starting from monotone schemes violating a Lipschitz condition for the Hamiltonian classes of numerical approximations are derived. Several numerical examples document the features of the presented methods. \(\copyright\) Academic Press.
Reviewer: Th.Sonar (Hamburg)
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L15 | Initial value problems for second-order hyperbolic equations |
Keywords:
upwind discretization; Petrov-Galerkin methods; Hamilton-Jacobi equations; level set methods; level set equations; numerical examplesReferences:
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