Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations

Editors: Gabriel R. Barrenechea, Franco Brezzi, Andrea Cangiani, Emmanuil H. Georgoulis



The authors are the leading experts in the field. It is hard to find such a selected list of authors writing about the developments they are carrying out at present

The main developments in recent approaches to numerical PDEs are gathered in this book

The survey nature of each contribution makes the volume an ideal reading for practitioners, academics, as well as graduate students wishing to grasp the fundamental aspect of modern numerical PDE approaches

This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches.

The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

Table of contents

Front Matter

Numerical Homogenization Methods for Parabolic Monotone Problems

Virtual Element Implementation for General Elliptic Equations

On Quasi-Interpolation Operators in Spline Spaces

Stabilised Finite Element Methods for Ill-Posed Problems with Conditional Stability

Static Condensation, Hybridization, and the Devising of the HDG Methods

Robust DPG Methods for Transient Convection-Diffusion

A Review of Hybrid High-Order Methods: Formulations, Computational Aspects, Comparison with Other Methods

A Survey of Trefftz Methods for the Helmholtz Equation

Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains

Discretization of Mixed Formulations of Elliptic Problems on Polyhedral Meshes

Variational Multiscale Stabilization and the Exponential Decay of Fine-Scale Correctors

Discontinuous Galerkin Methods for Time-Dependent Convection Dominated Problems: Basics, Recent Developments and Comparison with Other Methods

Foundations of the MHM Method

Back Matter