科研之友
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摘要
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.
- 出版日期2014
