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

Comput. Visual Sci. 9 (2006) 57-69 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...

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Bibliographic Details
Main Authors Bornemann, Folkmar, Rasch, Christian
Format Journal Article
LanguageEnglish
Published 30.03.2004
Subjects
Mathematics - Numerical Analysis
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Summary:Comput. Visual Sci. 9 (2006) 57-69 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.
DOI:10.48550/arxiv.math/0403517