TY - JOUR
T1 - A Stopping Criterion for Higher-Order Sweeping Schemes for Static Hamilton-Jacobi Equations
AU - Susana Serna & Jianliang Qian
JO - Journal of Computational Mathematics
VL - 4
SP - 552
EP - 568
PY - 2010
DA - 2010/08
SN - 28
DO - http://doi.org/10.4208/jcm.1003-m0016
UR - https://global-sci.org/intro/article_detail/jcm/8536.html
KW - Fast sweeping methods, Gauss-Seidel iteration, High order accuracy, Static
Hamilton-Jacobi equations, Eikonal equations.
AB - <p style="text-align: justify;">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.</p>