Finite-element Discretization of Static Hamilton-Jacobi Equations based on a Local Variational Principle
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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.
KeywordsHamilton–Jacobi equation Linear finite elements Local variational principle Viscosity solutions Compatibility condition Hopf–Lax formula Eikonal equation Adaptive Gauss–Seidel iteration
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