Volume 33, Issue 3
Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions

Kwangil KimYonghai Li

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

Published online: 2015-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

kkijgr@163.com (Kwangil Kim)

yonghai@jlu.edu.cn (Yonghai Li)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-227, author = {Kim , Kwangil and Li , Yonghai}, title = {Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1411-m4406}, url = {http://global-sci.org/intro/article_detail/jcm/9839.html} }
TY - JOUR T1 - Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions AU - Kim , Kwangil AU - Li , Yonghai JO - Journal of Computational Mathematics VL - 3 SP - 227 EP - 247 PY - 2015 DA - 2015/06 SN - 33 DO - http://doi.org/10.4208/jcm.1411-m4406 UR - https://global-sci.org/intro/article_detail/jcm/9839.html KW - Hamilton-Jacobi equations, Dirichlet boundary conditions, Finite volume, Monotone schemes. AB -

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.

Kwangil Kim & Yonghai Li. (2020). Convergence of Finite Volume Schemes for Hamilton-Jacobi Equations with Dirichlet Boundary Conditions. Journal of Computational Mathematics. 33 (3). 227-247. doi:10.4208/jcm.1411-m4406
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