A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions

Abstract

We analyze a new Galerkin finite element method for numerically solving a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation parameter, of order ${h^{1/2}}$ in a global energy norm which is stronger than the ${L^2}$ norm. This order is optimal in this norm for our choice of trial functions.