Title:         Basic Principles of Mixed Virtual Element Methods

Authors:       Franco Brezzi, Richard S. Falk, and Donatella Marini

Status:        ESAIM: Math. Modelling and Num. Anal., published
               online December, 2013.

Abstract: The aim of this paper is to give a simple, introductory presentation
          of the extension of the Virtual Element Method to the discretization
          of $H(div)$-conforming vector fields (or, more generally, of
          $(n-1)-Cochains$). As we shall see, the methods presented here can be
          seen as extensions of the so-called BDM family to deal with more
          general element geometries (such as polygons with an almost arbitrary
          geometry). For the sake of simplicity, we limit ourselves to the
          2-dimensional case, with the aim of making the basic philosophy
          clear. However, we consider an arbitrary degree of accuracy $k$ (the
          Virtual Element analogue of dealing with polynomials of arbitrary
          order in the Finite Element Framework).