An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two- and three-dimensions.
This work is devoted to an adaptive mesh redistribution (AMR) method towards solving the nonlinear Hamilton-Jacobi equations. The approach is based on a non-conservative second-order interpolation on the updated adaptive grids and a class of monitor functions. The adaptive mesh methods transform a uniform mesh in the logical domain to cluster grid points at the regions of the physical domain where the solution or its derivative is singular or nearly singular. The formal second-order rate of convergence is preserved for the proposed AMR methods. Extensive numerical experiments are presented.
scientific article; zbMATH DE number 1957093
scientific article