On numerical approximation of the Hamilton-Jacobi-transport system   arising in high frequency approximations
  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. 
Yves Achdou, Fabio Camilli and Lucilla Corrias
math.AP math.NA