Basic principles of mixed Virtual Element Methods
1 IUSS-Pavia and IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy.
2 KAU, Jeddah, Saudi Arabia.
3 Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA.
4 Dipartimento di Matematica, Università di Pavia, and IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy.
Received: 2 June 2013
Revised: 27 October 2013
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).
Mathematics Subject Classification: 65N30 / 65N12 / 65N15 / 76R50
Key words: Mixed formulations / virtual elements / polygonal meshes / polyhedral meshes
© EDP Sciences, SMAI, 2014