A Robust Finite Difference Method for a Singularly Perturbed Degenerate Parabolic Problems, Part I

Abstract

A singularly perturbed degenerate parabolic problem in one space dimension is considered. Bounds on derivatives of the solution are proved; these bounds depend on the two data parameters that determine how singularly perturbed and how degenerate the problem is. A tensor product mesh is constructed that is equidistant in time and of Shishkin type in space. A finite difference method on this mesh is proved to converge; the rate of convergence obtained depends on the degeneracy parameter but is independent of the singular perturbation parameter. Numerical results are presented.