Approximations for viscosity solutions of Hamilton-Jacobi equations with locally varying time and space grids

作者：Qian JL^*

来源：SIAM Journal on Numerical Analysis, 2006, 43(6): 2371-2401.

DOI：10.1137/04060682x

• local time-stepping
• error estimates
• monotone schemes
• Hamilton-Jacobi

A new monotone finite difference scheme is introduced that approximates viscosity solutions of first-order nonlinear Hamilton-Jacobi equations. The main feature of the scheme is that it allows for locally varying time and space grids, making it ideal for use with adaptive algorithms. Explicit a priori error estimates are given to establish convergence. Numerical examples, including adaptive mesh refinement examples, demonstrate the effectiveness of the proposed scheme.

• 出版日期2006