Uniform convergence of finite element method on Vulanović-Bakhvalov mesh for singularly perturbed convection–diffusion equation in 2D

Abstract

This paper investigates the uniform convergence of arbitrary order finite element methods on Vulanović-Bakhvalov mesh. We carefully design a new interpolation based on exponential layer structure, which not only overcomes the difficulties caused by the mesh step width, but also ensures the Dirichlet boundary condition. We successfully demonstrate the uniform convergence of the optimal order in the energy norm. The results of numerical experiments strongly validate our analysis.