This monograph is dedicated to the presentation of The Gradient Discretisation Method
(GDM) and to some of its applications. It is intended for masters students, researchers and …

We show convergence of a cell-centered finite volume discretization for linear elasticity. The
discretization, termed the MPSA method, was recently proposed in the context of geological …

Cell‐centered finite volume methods are prevailing in numerical simulation of flow in porous
media. However, due to the lack of cell‐centered finite volume methods for mechanics …

We derive equilibrated reconstructions of the Darcy velocity and of the total stress tensor for
Biot's poro-elasticity problem. Both reconstructions are obtained from mixed finite element …

The gradient scheme framework provides a unified analysis setting for many different
families of numerical methods for diffusion equations. We show in this paper that the …

We explain how to derive a network element for the linear elasticity problem. After
presenting sufficient conditions on the network for the validity of a discrete Korn inequality …

This thesis analyzes, at the continuous and at the discrete level on polyhedral meshes, the
scalar and the vector transport problems in three-dimensional domains. These problems are …

L'objet de cette thèse est l'étude et la mise en œuvre d'une méthode d'éléments finis multi-
échelles pour la simulation d'écoulements miscibles en milieux poreux. La définition des …

In this manuscript we focus on novel discretization schemes for solving the coupled
equations of poroelasticity and we present analytical and numerical results for …