A Uniformly Accurate Finite Element Method for a Singular Perturbation Problem in Conservative Form

Abstract

A Petrov–Galerkin finite element method with exponential basis elements is applied to a nonselfadjoint singularly perturbed two-point boundary value problem in conservative form. It is shown to be uniformly first order accurate in $L_\infty $ and is uniformly second order accurate at the nodes (i.e., the error constants are independent of the mesh size and the perturbation parameter).