Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions
Year: 2015
Author: Kwangil Kim, Yonghai Li
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 3 : pp. 227–247
Abstract
We study numerical methods for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. We first propose a new class of abstract monotone approximation schemes and get a convergence rate of 1/2 . Then, according to the abstract convergence results, by newly constructing monotone finite volume approximations on interior and boundary points, we obtain convergent finite volume schemes for time-dependent Hamilton-Jacobi equations with weak Dirichlet boundary conditions. Finally give some numerical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1411-m4406
Journal of Computational Mathematics, Vol. 33 (2015), Iss. 3 : pp. 227–247
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Hamilton-Jacobi equations Dirichlet boundary conditions Finite volume Monotone schemes.