We consider the Hamilton-Jacobi equation of eikonal type
where is convex and is allowed to be discontinuous. Under a suitable assumption on 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.
Cite this article
Charles M. Elliott, Klaus Deckelnick, Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities. Interfaces Free Bound. 6 (2004), no. 3, pp. 329–349DOI 10.4171/IFB/103