Streamline diffusion finite element method for a singularly perturbed problem with an interior layer on Shishkin mesh

Abstract

With the continuous development of science and technology, singularly perturbed problems have attracted more and more attentions from computational fluid scholars. In this paper, we discuss a singularly perturbed convection–diffusion problem with a discontinuous convection. Generally speaking, due to this discontinuity, an interior layer appears in the solution. A streamline diffusion finite element method on Shishkin mesh is used to solve this problem, and the optimal order of convergence in a modified streamline diffusion norm is derived. Numerical results are presented to support the theoretical conclusion.