High-resolution nonoscillatory central schemes for Hamilton-Jacobi equations

In this paper, we construct second-order central schemes for multidimension al Hamilton Jacobi equations and we show that they are nonoscillatory in th e sense of satisfying the maximum principle. Thus, these schemes provide th e rst examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are performed; L-1/L-in finity-errors and convergence rates are calculated. For convex Hamiltonians , numerical evidence con rms that our central schemes converge with second- order rates, when measured in the L-1-norm advocated in our recent paper [N umer. Math, to appear]. The standard L-infinity-norm, however, fails to det ect this second-order rate.