Non-oscillatory methods for relaxation approximation of Hamilton–Jacobi equations

摘要

In this paper, a class of high order non-oscillatory methods based on relaxation approximation for solving Hamilton–Jacobi equations is presented. The relaxation approximation transforms the nonlinear weakly hyperbolic equations to a semilinear strongly hyperbolic system with linear characteristic speeds and stiff source terms. The main ideas are to apply the weighted essentially non-oscillatory (WENO) reconstruction for the spatial discretization and an implicit–explicit method for the temporal integration. To illustrate the performance of the method, numerical results are carried out on several test problems for the two-dimensional Hamilton–Jacobi equations with both convex and nonconvex Hamiltonians.