The streamline-diffusion finite element method on graded meshes for a convection–diffusion problem

Abstract

In this paper, the streamline-diffusion finite element method is applied to a two-dimensional convection–diffusion problem posed on the unit square, using a graded mesh of O(N2) points based on standard Lagrange polynomials of degree k≥1. We prove the method is convergent almost uniformly in the perturbation parameter ϵ, and a convergence order O(N−klogk+1⁡(1ϵ)) is obtained in a streamline-diffusion norm under certain assumptions. Numerical experiments support the theoretical results.