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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).
@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 },
pages = {1227--1240},
publisher = {EDP-Sciences},
volume = {48},
number = {4},
year = {2014},
doi = {10.1051/m2an/2013138},
mrnumber = {3264352},
zbl = {1299.76130},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013138/}
}
TY - JOUR AU - Brezzi, F. AU - Falk, Richard S. AU - Donatella Marini, L. TI - Basic principles of mixed Virtual Element Methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1227 EP - 1240 VL - 48 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013138/ DO - 10.1051/m2an/2013138 LA - en ID - M2AN_2014__48_4_1227_0 ER -
%0 Journal Article %A Brezzi, F. %A Falk, Richard S. %A Donatella Marini, L. %T Basic principles of mixed Virtual Element Methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1227-1240 %V 48 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2013138/ %R 10.1051/m2an/2013138 %G en %F 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 , Tome 48 (2014) no. 4, pp. 1227-1240. doi: 10.1051/m2an/2013138
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