High-Resolution Nonoscillatory Central Schemes for Hamilton-Jacobi Equations

In this paper, we construct second-order central schemes for multidimensional Hamilton–Jacobi equations and we show that they are nonoscillatory in the sense of satisfying the maximum principle. Thus, these schemes provide the first examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are performed; L1/L∞-errors and convergence rates are calculated. For convex Hamiltonians, numerical evidence confirms that our central schemes converge with second-order rates, when measured in the L1-norm advocated in our recent paper [Numer. Math, to appear]. The standard L∞-norm, however, fails to detect this second-order rate.