A STOPPING CRITERION FOR HIGHER-ORDER SWEEPING SCHEMES FOR STATIC HAMILTON-JACOBI EQUATIONS

作     者：Susana Serna Jianliang Qian 

作者机构：Department of Mathematics University of California Los Angeles CA 90095 USA Department de Matematiques Universitat Autonoma de Barcelona 8193 Bellaterra Spain Department of Mathematics Michigan State University East Lansing MI 48824 USA 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2010年第28卷第4期

页      面：552-568页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by DGICYT MTM2008-03597 Ramon y Cajal Program supported by NSF DMS # 0810104 

主　　题：Fast sweeping methods Gauss-Seidel iteration High order accuracy Static Hamilton-Jacobi equations Eikonal equations. 

摘      要：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.