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Basic principles of mixed virtual element methods (Articolo in rivista)

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Basic principles of mixed virtual element methods (Articolo in rivista) (literal)

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F. Brezzi; Richard S. Falk; L. Donatella Marini (2014)
Basic principles of mixed virtual element methods
in Modélisation mathématique et analyse numérique (En ligne); EDP Sciences, Les Ulis Cedex (Francia)
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http://journals.cambridge.org/download.php?file=%2FMZA%2FMZA48_04%2FS0764583X13001386a.pdf&code=930637c4eabf31b75e74d9e8bd98cb77 (literal)

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IUSS-Pavia, Italy; IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy; KAU, Jeddah, Saudi Arabia; Department of Mathematics, Rutgers University, Piscataway, NJ 08854, United States; Dipartimento di Matematica, Università di Pavia; (literal)

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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). (literal)

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