BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS

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 elds (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). 1991 Mathematics Subject Classication. 65N30,65N12,65G99,76R99. The dates will be set by the publisher