High-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations

Abstract

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; $L^1$/$L^{\infty}$-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 $L^{\infty}$-norm, however, fails to detect this second-order rate.