Preprint 2000-034

Convergence Results for an Inhomogeneous System Arising in Various High Frequency Approximations

Laurent Gosse and Francois James

Abstract: 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, <>
Francois James, <>
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<> July 31 2000.

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