Finite-element discretization of static Hamilton-Jacobi equations based on a local variational principle

Folkmar Bornemann, Christian Rasch

Research output: Contribution to journalArticlepeer-review

71 Scopus citations

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.

Original languageEnglish
Pages (from-to)57-69
Number of pages13
JournalComputing and Visualization in Science
Volume9
Issue number2
DOIs
StatePublished - Jul 2006

Keywords

  • Adaptive Gauss-Seidel iteration
  • Compatibility condition
  • Eikonal equation
  • Hamilton-Jacobi equation
  • Hopf-Lax formula
  • Linear finite elements
  • Local variational principle
  • Viscosity solutions

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