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Numerical schemes for Hamilton-Jacobi equations on unstructured meshes. (English) Zbl 1029.65111

The finite element method is applied to the viscosity solutions of the Hamilton-Jacobi equations on unstructured meshes. A new numerical scheme is constructed by improving the finite element scheme. Under certain limitations both solutions converge to the viscosity solutions of the Hamilton-Jacobi equations. The new scheme has weaker restrictions for the convergence.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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