On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations

preprint2011arXivOpen access

Abstract

In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and the convergence of the approximated solution toward the viscosity-measure valued solution of the exact problem.

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