A Class of High Resolution Difference Schemes for Nonlinear Hamilton-Jacobi Equations with Varying Time and Space Grids

摘要: Based on a simple projection of the solution increments underlying partial differential equations (PDEs) at each local time level, this paper presents difference scheme for nonlinear Hamilton--Jacobi (H--J) with varying and space grids. The is good consistency monotone under CFL-type condition. Moreover, one may deduce conservative step similar to Osher Sanders approximating hyperbolic conservation law (CL) from our according close relation between CLs H--J equations. Second order accurate schemes are constructed by combining reconstruction technique second Runge--Kutta discretization or Lax--Wendroff type method. They keep some properties global schemes, including stability convergence, can be applied solve numerically initial-boundary-value problems viscous also suitable parallel computing. Numerical errors experimental rate convergence in Lp-norm, p = 1, 2, $\infty$, obtained several one- two-dimensional problems. results show that present higher accuracy.