A Novel Nonconforming Uniformly Convergent Finite Element Method in Two Dimensions

We give a new analysis of a nonconforming Galerkin finite element method for solving linear elliptic singularly perturbed boundary value problems for rectangular domains. In the case of ordinary boundary layers the method is shown to be convergent uniformly with respect to the perturbation parameter of order h1r2 in the energy norm. The trial functions are exponentials fitted to the differential operator.