We consider the stationary Hamilton-Jacobi equation Sigma(N)(i,j=1) b(ij) (x)u(xi) u(xj) = [f(x)](2), in Omega, where Omega is an open set of R-n, b can vanish at some points, and the right- hand- side f is strictly positive and is allowed to be discontinuous. More precisely, we consider a special class of discontinuities for which the notion of viscosity solution is well- suited. We propose a semi- Lagrangian scheme for the numerical approximation of the viscosity solution in the sense of Ishii and we study its properties. We also prove an a priori error estimate for the scheme in L-1. The last section contains some applications to control and image processing problems.
AN APPROXIMATION SCHEME FOR AN EIKONAL EQUATION WITH DISCONTINUOUS COEFFICIENT / Adriano, Festa; Falcone, Maurizio. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 52:1(2014), pp. 236-257. [10.1137/120901829]
AN APPROXIMATION SCHEME FOR AN EIKONAL EQUATION WITH DISCONTINUOUS COEFFICIENT
FALCONE, Maurizio
2014
Abstract
We consider the stationary Hamilton-Jacobi equation Sigma(N)(i,j=1) b(ij) (x)u(xi) u(xj) = [f(x)](2), in Omega, where Omega is an open set of R-n, b can vanish at some points, and the right- hand- side f is strictly positive and is allowed to be discontinuous. More precisely, we consider a special class of discontinuities for which the notion of viscosity solution is well- suited. We propose a semi- Lagrangian scheme for the numerical approximation of the viscosity solution in the sense of Ishii and we study its properties. We also prove an a priori error estimate for the scheme in L-1. The last section contains some applications to control and image processing problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
