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Basic principles of mixed Virtual Element Methods

Published online by Cambridge University Press:  15 July 2014

F. Brezzi ,
Richard S. Falk  and
L. Donatella Marini
F. Brezzi
Affiliation:
IUSS-Pavia and IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy.. brezzi@imati.cnr.it KAU, Jeddah, Saudi Arabia.
Richard S. Falk
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA.; falk@math.rutgers.edu
L. Donatella Marini
Affiliation:
Dipartimento di Matematica, Università di Pavia, and IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy.; marini@imati.cnr.it
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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).

Keywords

Mixed formulationsvirtual elementspolygonal meshespolyhedral meshes

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 4 , July 2014 , pp. 1227 - 1240
Copyright
© EDP Sciences, SMAI, 2014

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