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 …

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 …

Hybrid High-Order (HHO) methods attach discrete unknowns to the cells and to the faces of
the mesh. At the heart of their devising lie two intuitive ideas:(i) a local operator …

Since its introduction, the virtual element method (VEM) was shown to be able to deal with a
large variety of polygons, while achieving good convergence rates. The regularity …

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of
elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same …

We present the design, convergence analysis and numerical investigations of the
nonconforming virtual element method with Streamline Upwind/Petrov–Galerkin (VEM …

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of
(linear and) nonlinear elasticity models in the small deformation regime which are of …

We devise and analyze two hybrid high-order (HHO) methods for the numerical
approximation of the biharmonic problem. The methods support polyhedral meshes, rely on …

In this work we propose a novel Hybrid High-Order method for the incompressible Navier–
Stokes equations based on a formulation of the convective term including Temam's device …

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic
materials undergoing finite deformations. The HHO methods use as discrete unknowns …