Propagation of graphs in two-dimensional inhomogeneous media

Authors:
Klaus Deckelnick;Charles M. Elliott
Affiliations:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany;Department of Mathematics, University of Sussex, Falmer, Brighton, UK
Venue:
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Year:
2006

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Abstract

We consider the propagation of a front in a two-dimensional striated medium. In the case of a front that can be written as a graph over the real line we are led to an Eikonal equation for the height function which contains a possibly discontinuous coefficient. We prove existence and uniqueness of a viscosity solution in the sense of Ishii. Furthermore, we obtain an O(√h)-error bound for a monotone and consistent finite difference scheme. We conclude with some numerical tests.