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

Whitney forms are widely known as finite elements for differential forms. Whitney's original
definition yields first order functions on simplicial complexes, and a lot of research has been …

In this paper, we present a novel arbitrary-order discrete de Rham (DDR) complex on
general polyhedral meshes based on the decomposition of polynomial spaces into ranges …

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 …

In this work, merging ideas from compatible discretisations and polyhedral methods, we
construct novel fully discrete polynomial de Rham sequences of arbitrary degree on …

We construct 2D and 3D finite element de Rham sequences of arbitrary polynomial degrees
with extra smoothness. Some of these elements have nodal degrees of freedom and can be …

We develop a theory of finite element systems, for the purpose of discretizing sections of
vector bundles, in particular those arising in the theory of elasticity. In the presence of …

This thesis presents a new class of spatial discretization schemes on polyhedral meshes,
called Compatible Discrete Operator (CDO) schemes and their application to elliptic and …

We introduce the family of trimmed serendipity finite element differential form spaces,
defined on cubical meshes in any number of dimensions, for any polynomial degree, and for …

Explicit generators for high-order (r> 1) scalar and vector finite element spaces generally
used in numerical electromagnetism are presented and classical degrees of freedom, the so …