Convergence Results for an Inhomogeneous System Arising in Various High
Laurent Gosse and Francois James
This paper is devoted to both theoretical and numerical study of a system
involving an eikonal equation of Hamilton-Jacobi type and a linear
conservation law as it comes out
of the geometrical optics expansion of the wave equation or the semiclassical
limit for the Schr\"odinger equation. We first state an existence and
uniqueness result in the framework of viscosity and duality solutions. Then
we study the behavior of some classical numerical schemes on this problem
and we give sufficient conditions to ensure convergence. As an illustration,
some practical computations are provided.
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- Laurent Gosse,
- Publishing information:
- Submitted by:
July 31 2000.
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