Robust exponential convergence of finite element methods for problems with boundary and interior layers

Abstract

The hp version of the finite element method for a one-dimensional, singularly perturbed elliptic-elliptic model problem with piecewise defined analytic input data is considered. It is shown that the use of piecewise polynomials of degree p on a mesh consisting of two 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.