Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

Numerical methods with discrete conservation statements are useful because they cannot
produce solutions that violate important physical constraints. A large number of numerical …

Abstract Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …

The objective of this paper is to present an approach to electromagnetic field simulation
based on the systematic use of the global (ie integral) quantities. In this approach, the …

In this paper we apply the ideas of algebraic topology to the analysis of the finite volume and
finite element methods, illuminating the similarity between the discretization strategies …

We show that the equations of electromagnetism can be directly obtained in a finite form, ie,
discrete, thus avoiding the traditional discretization methods of Maxwell's differential …

Applied mathematical modeling is concerned with solving unsteady problems. Splitting
schemes are attributed to the transition from a complex problem to a chain of simpler …

An investigation on the reason for analogies between physical theories is carried out. The
reason is found in the fact that in every physical theory there are basic physical quantities …

This book is an outgrowth of my involvement in two groups of research in solid mechanics,
created in 1960 for the French nuclear energy program. At this time, it was decided that …

Solid modeling is a consistent set of principles for mathematical and computer modeling of
three-dimensional solids. The collection evolved over the last thirty years, and is now mature …