Basic principles of mixed Virtual Element Methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 4, p. 1227-1240
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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 : https://doi.org/10.1051/m2an/2013138
Classification:  65N30,  65N12,  65N15,  76R50
Keywords: mixed formulations, virtual elements, polygonal meshes, polyhedral meshes
@article{M2AN_2014__48_4_1227_0,
     author = {Brezzi, F. and Falk, Richard S. and Donatella Marini, L.},
     title = {Basic principles of mixed Virtual Element Methods},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     pages = {1227-1240},
     doi = {10.1051/m2an/2013138},
     zbl = {1299.76130},
     mrnumber = {3264352},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_4_1227_0}
}
Brezzi, F.; Falk, Richard S.; Donatella Marini, L. Basic principles of mixed Virtual Element Methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 4, pp. 1227-1240. doi : 10.1051/m2an/2013138. http://www.numdam.org/item/M2AN_2014__48_4_1227_0/

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