Finite element methods have been the subject of active research for the last six decades.
However, gaps remain in the understanding of even the simplest applications, including …

This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

This textbook has grown out of a course which we teach periodically at the University of
Iowa. We have beginning graduate students in mathematics who wish to work in numerical …

The main purpose of this monograph is to provide a simple and accessible introduction to
the mixed finite element method as a fundamental tool to numerically solve a wide class of …

This article reports on the confluence of two streams of research, one emanating from the
fields of numerical analysis and scientific computation, the other from topology and …

We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes
having test function spaces that are automatically computable to guarantee stability. Given a …

The Kolmogorov N-width d N (M) describes the rate of the worst-case error (wrt a subset M⊂
H of a normed space H) arising from a projection onto the best-possible linear subspace of …