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

Yves Achdou (1) , Fabio Camilli (2) , Lucilla Corrias (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
3 UEVE - Université d'Évry-Val-d'Essonne

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.

Domaines: Analyse numérique [cs.NA]

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, 2014, 19 (3), pp.629 - 650. ⟨10.3934/dcdsb.2014.19.629⟩. ⟨hal-01456509⟩