A Mesh Refinement Algorithm for Singularly Perturbed Boundary and Interior Layer Problems

Abstract

A robust automated mesh refinement algorithm is proposed for numerical solution of singularly perturbed boundary and interior layer problems. The proposed algorithm is heuristically based on two smoothness indicators which are functions of consecutive differences of the computed solution on a given mesh. The main salient features of the proposed heuristic mesh generation algorithm are: (i) it does not require a priori knowledge about the nature or location of the layered region, (ii) it is independent of the problem under consideration and the underlying numerical scheme. The proposed algorithm is applied to solve a wide range of 1D as well as 2D test problems to show its robustness.