Superconvergence Using Pointwise Interpolation in Convection-Diffusion Problems

Considering a singularly perturbed convection-diffusion problem, we present an analysis for a superconvergence result using pointwise interpolation of Gau{\ss}-Lobatto type for higher-order streamline diffusion FEM. We show a useful connection between two different types of interpolation, namely a vertex-edge-cell interpolant and a pointwise interpolant. Moreover, different postprocessing operators are analysed and applied to model problems.Comment: 19 page

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

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 paramete

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield