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CONVERGENCE OF FINITE VOLUME SCHEMES FOR HAMILTON-JACOBI EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

CONVERGENCE OF FINITE VOLUME SCHEMES FOR HAMILTON-JACOBI EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS
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摘要 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. 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.
作者 Kwangil Kim Yonghai Li
机构地区 School of Mathematics Department of Mathematics
出处 《Journal of Computational Mathematics》 SCIE CSCD 2015年第3期227-247,共21页 计算数学（英文）
基金 Acknowledgments. This work was supported by the National Natural Science Foundation of China （No. 11371170）.
关键词 Hamilton-Jacobi equations Dirichlet boundary conditions Finite volume Monotone schemes. Hamilton-Jacobi equations, Dirichlet boundary conditions, Finite volume, Monotone schemes.
分类号 O175.26 [理学—基础数学] O35 [理学—流体力学]
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Journal of Computational Mathematics
2015年 第3期

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