About 10 years ago, Mixed and Hybrid Finite Element Methods by F. Brezzi and M. Fortin
went out of print and we were asked to allow a second printing. The world had evolved and …

Since the middle of the last century, computing power has increased sufficiently that the
direct numerical approximation of Maxwell's equations is now an increasingly important tool …

In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the
Laplacian to various forms of boundary integral equations based on the direct approach …

In this paper, we develop and analyze a general approach to preconditioning linear systems
of equations arising from conforming finite element discretizations of H (curl,)-and H (div,) …

This book arose from lectures on Maxwell's equations given by the authors between 2007
and 2013. Graduate students from pure and applied mathematics, physics—including …

In the past decade, the mathematics of superconductivity has been the subject of intense
study. This book examines in detail the nonlinear Ginzburg–Landau (GL) functional, the …

This book offers a thorough and self-contained exposition of the mathematics of time-domain
boundary integral equations associated to the wave equation, including applications to …

Computational methods to approximate the solution of differential equations play a crucial
role in science, engineering, mathematics, and technology. Indeed, the key processes which …

The fields of photonics and phononics encompass the fundamental science of light and
sound propagation and interactions in complex structures, as well as its technological …

This paper contains two major contributions. First we derive, following the discrete de Rham
(DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes …