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 …

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 …

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

In the last few decades the concepts of structure-preserving discretization, geometric
integration and compatible discretizations have emerged as subfields in the numerical …

The classical Cauchy continuum theory is suitable to model highly homogeneous materials.
However, many materials, such as porous media or metamaterials, exhibit a pronounced …

We provide both a general framework for discretizing de Rham sequences of differential
forms of high regularity, and some examples of finite element spaces that fit in the …

Coupling the mimetic finite difference method with the tensor-train format results in a very
effective method for low-rank numerical approximations of the solutions of the time …

We construct mollification operators in strongly Lipschitz domains that do not invoke non-
trivial extensions, are Lp stable for any real number p∈[1,∞], and commute with the …

We derive H (curl)-error estimates and improved L 2-error estimates for the Maxwell
equations approximated using edge finite elements. These estimates only invoke the …