J. Comp. Math., 33 (2015), pp. 227-247.


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

Kwangil Kim 1, Yonghai Li 2

1 School of Mathematics, Jilin University, Changchun 130012, China; Department of Mathematics, University of Science, Pyongyang, DPR Korea
2 School of Mathematics, Jilin University, Changchun 130012, China

Received 2013-6-26 Accepted 2014-11-17
Available online 2015-5-15
doi:10.4208/jcm.1411-m4406

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.

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

AMS subject classifications: 65N30.


Email: kkijgr@163.com, yonghai@jlu.edu.cn
 

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