Two-Dimensional Interpolation of Functions with Large Gradients in Boundary Layers

Abstract

Question of two-dimensional interpolation of functions with large gradients in the boundary layers is considered. The problem is that an application of polynomial interpolation on an uniform mesh to functions with large gradients leads to significant errors. We consider two approaches for increase of accuracy of interpolation: a fitting of the interpolation formula to a boundary layer component and the application of polynomial interpolation on Shishkin mesh. Numerical results are discussed.