Seminario di Analisi Numerica: “The Virtual Element Method and the connection with the Mimetic Finite Difference method”

Martedì 13 Dicembre 2016, ore 12:30 - Sala Riunioni VII Piano 1BC45 - Gianmarco Manzini


Martedì 13 Dicembre 2016 alle ore 12:30 in Sala Riunioni VII Piano 1BC45, Gianmarco Manzini (Los Alamos, USA - IMATI-CNR, Pavia) terrà un seminario dal titolo VThe Virtual Element Method and the connection with the Mimetic Finite Difference method”.

In this talk we present the Virtual Element Method (VEM) for the numerical discretization of Partial Differential Equations, and, in particular for elliptic problems. The VEM is an extension of the Finite Element Method (FEM) that is particularly suited for unstructured meshes of polygonal (2D) and polyhedral (3D) cells. Although the VEM has been proposed to the community of researchers only very recently (the founding paper was published in 2013) a massive amount of research work has led to the development of different formulation (conforming, nonconforming, mixed) and the application to different kind of model problems (advection-reaction-diffusion, Stokes and biharmonic equations). The VEM is a variational reformulation of the pre-existing arbitrary-order Mimetic Finite Difference method (MFD), and inherits from this latter a few properties, such as the polynomial consistency and spectral stability, that are crucial for high-order accuracy, well-posedness, and robustness. Both the VEM and the MFD methods are families of schemes which have been shown to be successful and competitive with respect to schemes from similar alternative formulations working on polygonal and polyhedral discretizations, as for example PFEM, HHO, HDG, weak Galerkin. The connection between VEM and MFD is discussed in the talk.