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 …

Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlap** control volumes. Degrees of …

We present, on the simplest possible case, what we consider as the very basic features of
the (brand new) virtual element method. As the readers will easily recognize, the virtual …

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 original virtual element space with degree of accuracy k, projector operators in the H 1-
seminorm onto polynomials of degree≤ k can be easily computed. On the other hand …

We discuss the application of virtual elements to linear elasticity problems, for both the
compressible and the nearly incompressible case. Virtual elements are very close to mimetic …

We consider the discretization of a boundary value problem for a general linear second-
order elliptic operator with smooth coefficients using the Virtual Element approach. As in [AH …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …