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

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

2011-10-19

arxiv.org/abs/1110.4291v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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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