Building bridges: Connections and challenges in modern approaches to numerical partial differential equations

This volume contains survey articles from the topics of a number of the plenary talks of the 101st LMS-EPSRC Symposium entitled Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations held at Durham University between 8 and 16 July 2014. The symposium was devoted to recent advances in numerical methods for partial differential equations (PDEs) using non-polynomial basis functions, mimetic finite difference methods, and discontinuous Galerkin (dG) methods. Moreover, since recent works in these directions have highlighted unforeseen pairwise connections between the different approaches, a particular emphasis in this symposium has been to explore further links and to exchange ideas and techniques between them.