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 - <p style="text-align: justify;">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.</p>