High-order finite element method on a Vulanović–Bakhvalov mesh for a singularly perturbed convection–diffusion problem

Abstract

A kth order (k≥1) finite element method on a Vulanović–Bakhvalov mesh is proposed for a singularly perturbed convection–diffusion problem. Some properties of the Vulanović–Bakhvalov mesh are derived. Based on these estimations and a new Lagrange interpolation technique, an optimal order of uniform convergence with respect to the perturbation parameter is proved. Numerical results are provided to demonstrate the theoretical findings.