Supercloseness analysis of the linear finite element method for a singularly perturbed convection–diffusion problem on Vulanović–Bakhvalov mesh

Abstract

Vulanović–Bakhvalov mesh is a kind of Bakhvalov-type mesh, which has the advantages of good numerical convergence and the transition point between coarse and fine mesh is not affected by mesh parameters. However, there is little theory of finite element methods for this mesh. In this paper, a linear finite element method on a Vulanović–Bakhvalov mesh is studied for a singularly perturbed convection–diffusion problem. In this process, some properties of the Vulanović–Bakhvalov mesh are obtained. Based on these properties and a new Lagrange interpolation, we further derive the supercloseness result of 3/2th order in an energy norm.