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.
ON NUMERICAL APPROXIMATION OF THE HAMILTON-JACOBI-TRANSPORT SYSTEM ARISING IN HIGH FREQUENCY APPROXIMATIONS / Yves, Achdou; Camilli, Fabio; Lucilla, Corrias. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:3(2014), pp. 629-650. [10.3934/dcdsb.2014.19.629]
ON NUMERICAL APPROXIMATION OF THE HAMILTON-JACOBI-TRANSPORT SYSTEM ARISING IN HIGH FREQUENCY APPROXIMATIONS
CAMILLI, FABIO;
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
