On the robust exponential convergence of hp finite element methods for problems with boundary layers

Abstract

The hp version of the finite element method for a one-dimensional, singularly perturbed elliptic-elliptic model problem with analytic input data is considered. It is shown that the use of piecewise polynomials of degree p on a mesh consisting of three suitably chosen elements leads to robust exponential convergence, i.e., the exponential rate of convergence depends only on the input data and is independent of the perturbation parameter.