Relaxation Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations

This paper presents a relaxation Lax-Friedrichs sweeping scheme to approximate viscosity solutions of static Hamilton Jacobi equations in any number of spatial dimensions. It is a generalization of the scheme proposed in Kao et al. (J Comput Phys 196:367–391, 2004). Numerical examples suggest that the relaxation Lax-Friedrichs sweeping scheme has smaller number of iterations than the original Lax-Friedrichs sweeping scheme when the relaxation factor ω is slightly larger than one. And first order convergence is also demonstrated by numerical results. A theoretical analysis for our scheme in a special case is given.