Basic principles of mixed Virtual Element Methods

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

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

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

Abstract

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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).

How to cite

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Brezzi, 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 -

References

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