Interfaces and Free Boundaries
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Published online: 2004-09-30
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuitiesKlaus Deckelnick and Charles M. Elliott (1) Otto-von-Guericke-Universität Magdeburg, Germany
(2) University of Warwick, Coventry, UK
We consider the Hamilton-Jacobi equation of eikonal type $$H(\nabla u) = f(x), \quad x \in \Omega,$$ where $H$ is convex and $f$ is allowed to be discontinuous. Under a suitable assumption on $f$ we prove a comparison principle for viscosity sub- and supersolutions in the sense of Ishii. Furthermore, we develop an error analysis for a class of finite difference schemes, which are monotone, consistent and satisfy a suitable stability condition.
Keywords: Hamiton-Jacobi equation, viscosity solution, comparison principle, finite difference method, error bounds
Deckelnick Klaus, Elliott Charles: Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Interfaces Free Bound. 6 (2004), 329-349. doi: 10.4171/IFB/103