Approximations for Viscosity Solutions of Hamilton-Jacobi Equations With Locally Varying Time and Space Grids

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.

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