An analysis of a conforming exponentially fitted finite element method for a convection–diffusion problem

In this paper, we present a convergence analysis for a conforming exponentially fitted Galerkin finite element method with triangular elements for a linear singularly perturbed convection–diffusion problem with a singular perturbation parameter ε. It is shown that the error for the finite element solution in the energy norm is bounded by O(h(ε1/2||u||2+ε−1/2||u||1)) if a regular family of triangular meshes is used. In the case that a problem contains only exponential boundary layers, the method is shown to be convergent at a rate of h1/2+h|ln ε| on anisotropic layer-fitted meshes.