JournalsifbVol. 6 , No. 3DOI 10.4171/ifb/103

Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities

  • Charles M. Elliott

    University of Warwick, Coventry, UK
  • Klaus Deckelnick

    Otto-von-Guericke-Universität Magdeburg, Germany
Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuities cover

Abstract

We consider the Hamilton-Jacobi equation of eikonal type

H(u)=f(x),xΩ,H(\nabla u) = f(x), \quad x \in \Omega,

where HH is convex and ff is allowed to be discontinuous. Under a suitable assumption on ff 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.