Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions

Authors

  • Kwangil Kim School of Mathematics, Jilin University, Changchun 130012, China
  • Yonghai Li School of Mathematics, Jilin University, Changchun 130012, Jilin, China

DOI:

https://doi.org/10.4208/jcm.1411-m4406

Keywords:

Hamilton-Jacobi equations, Dirichlet boundary conditions, Finite volume, Monotone schemes.

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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Published

2018-08-22

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Issue

Vol. 33 No. 3 (2015)

Section

Articles

How to Cite

Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions. (2018). Journal of Computational Mathematics, 33(3), 227-247. https://doi.org/10.4208/jcm.1411-m4406