Basic principles of mixed Virtual Element Methods
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1227-1240.

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).

DOI : 10.1051/m2an/2013138
Classification : 65N30, 65N12, 65N15, 76R50
Mots-clés : mixed formulations, virtual elements, polygonal meshes, polyhedral meshes 
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Brezzi, F.; Falk, Richard S.; Donatella Marini, L. Basic principles of mixed Virtual Element Methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1227-1240. doi : 10.1051/m2an/2013138. http://www.numdam.org/articles/10.1051/m2an/2013138/

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