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

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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Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2014, 19 (3), pp.629 - 650. 〈10.3934/dcdsb.2014.19.629〉
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Soumis le : mercredi 22 août 2012 - 15:38:27
Dernière modification le : vendredi 31 août 2018 - 09:06:02

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Yves Achdou, Fabio Camilli, Lucilla Corrias. On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2014, 19 (3), pp.629 - 650. 〈10.3934/dcdsb.2014.19.629〉. 〈hal-00724771〉

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