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1 results

  • Basic principles of mixed Virtual Element Methods

  • F. Brezzi, Richard S. Falk, L. Donatella Marini
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 4 / July 2014
    Published online by Cambridge University Press:
    15 July 2014, pp. 1227-1240
    Print publication:
    July 2014

  • 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).