A Stopping Criterion for Higher-order Sweeping Schemes for Static Hamilton-Jacobi Equations

Susana Serna, Jianliang Qian

Type: Article

Publication Date: 2010-01-01

Citations: 27

DOI: https://doi.org/10.4208/jcm.1003-m0016

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Abstract

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.

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Journal of Computational Mathematics - View - PDF

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