# Basic principles of mixed Virtual Element Methods

F. Brezzi; Richard S. Falk; L. Donatella Marini

- Volume: 48, Issue: 4, page 1227-1240
- ISSN: 0764-583X

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topBrezzi, F., Falk, Richard S., and Donatella Marini, L.. "Basic principles of mixed Virtual Element Methods." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 1227-1240. <http://eudml.org/doc/273108>.

@article{Brezzi2014,

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 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).},

author = {Brezzi, F., Falk, Richard S., Donatella Marini, L.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {mixed formulations; virtual elements; polygonal meshes; polyhedral meshes},

language = {eng},

number = {4},

pages = {1227-1240},

publisher = {EDP-Sciences},

title = {Basic principles of mixed Virtual Element Methods},

url = {http://eudml.org/doc/273108},

volume = {48},

year = {2014},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 4

SP - 1227

EP - 1240

AB - 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).

LA - eng

KW - mixed formulations; virtual elements; polygonal meshes; polyhedral meshes

UR - http://eudml.org/doc/273108

ER -

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