A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations (Journal of Computational Mathematics, 2018)
We propose an effective stopping criterion for higher-order fast sweeping schemes for static Hamilton-Jacobi equations based on ratios of three consecutive iterations. To design the new stopping criterion we analyze the convergence of the first-order Lax-Friedrichs sweeping scheme by using the theory of nonlinear iteration. In addition, we propose a fifth-order Weighted PowerENO sweeping scheme for static Hamilton-Jacobi equations with convex Hamiltonians and present numerical examples that validate the effectiveness of the new stopping criterion.
Keywords: Fast sweeping methods; Gauss-Seidel iteration; High order accuracy; Static Hamilton-Jacobi equations; Eikonal equations.