Journal
COMPUTING AND VISUALIZATION IN SCIENCE
Volume 9, Issue 2, Pages 57-69Publisher
SPRINGER
DOI: 10.1007/s00791-006-0016-y
Keywords
Hamilton-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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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.
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