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Computing and Visualization in Science

, Volume 9, Issue 2, pp 57–69 | Cite as

Finite-element Discretization of Static Hamilton-Jacobi Equations based on a Local Variational Principle

  • Folkmar Bornemann
  • Christian Rasch
REGULAR ARTICLE

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.

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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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Center of Mathematics, M3Technical University of MunichMunichGermany

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