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Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

Folkmar Bornemann·Christian Rasch
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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.

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Folkmar Bornemann, Christian Rasch. 2004-03-30. Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle. https://doi.org/10.1007/s00791-006-0016-y

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