We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

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

The Hitchhiker's Guide to the Virtual Element Method | Mathematical Models and Methods in
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …

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 …

In the present paper we develop a new family of Virtual Elements for the Stokes problem on
polygonal meshes. By a proper choice of the Virtual space of velocities and the associated …

The virtual element method (VEM) is a recent technology that can make use of very general
polygonal/polyhedral meshes without the need to integrate complex nonpolynomial …

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

The numerical approximation of 2D elasticity problems is considered, in the framework of the
small strain theory and in connection with the mixed Hellinger–Reissner variational …

The focus of this paper is on developing a virtual element method (VEM) for Darcy and
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …

A posteriori error estimation and adaptivity are very useful in the context of the virtual
element and mimetic discretization methods due to the flexibility of the meshes to which …