Basic Principles of Mixed Virtual Element Methods By Prof. L. Donatella Marini (Universita di Pavia, Italy)

Overview

Abstract

We present, in the simplest possible way, the extension of the Virtual Element Method to the discretization of H(div)-conforming vector fields. 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). Preliminary numerical results are presented.

Brief Biography

L. Donatella Marini graduated in Mathematics at the University of Pavia in 1970, then was researcher of C.N.R. at the Istituto di Analisi Numerica in Pavia (now IMATI-CNR) from April 1, 1973 to October 31, 1990. After winning a professorship position in Numerical Analysis she joined the University of Genova from November 1, 1990 to October 31, 1993, and then she moved to the University of Pavia since November 1, 1993. Her scientific production consists of about 90 scientific papers, mainly on Numerical Methods for Partial Differential Equations: Finite elements of various kinds (conforming, non-conforming, hybrid, mixed, and in the last decade Discontinuous Galerkin methods) for different applications (semiconductor device simulation, electromagnetism, fluid-dynamics, structural mechanics). In the last year she was among the developers of a new methodology, the Virtual Element Method, particularly well suited for the approximation of Pde’s on polygonal/polyhedral meshes.

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http://www.imati.cnr.it/marini​