Franco Dassi (Universita' degli Studi di Milano Bicocca)

Thursday 5th March, 2020 14:00-15:00 Maths 311B


The Virtual Element Method (VEM) is a way to solve partial diffential equations that extends the Finite Element Method (FEM) to polygonal/polihedral meshes [1, 2]. To better understand the idea behind such method, we describe VEM in the simplest case, a standard Laplacian problem. Then, we give some detail on how the flexibility of VEM was already exploited to deal with curved elements and to get high regularity or divergence-free numerical solutions. There are a lot of appications that requires such characteritstics on the distrete solution. Consider, for instance, a flow-problem which is described via Stokes or Navier-Stokes equations. The VEM discrete solution satisfies the incompressibility condition on the flow point-wise, i.e., the solution has point-wise null divergence. Moreover, there are a lot of applications characterized by curved domains, for instance the thick-walled viscoelastic cylinder or the perforated plastic plate in solid mechanics applications or wings in aerodynamic flow computations. At the end of the talk we show some numerical results both in two and three dimensions that validate this new approach for both the theoretical and practical point of views.


[1] L. Beir˜ao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo. Basic principles of virtual element methods. Mathematical Models and Methods in Applied Sciences, 23(01):199–214, 2013.

[2] L. Beir˜ao da Veiga, F. Brezzi, L. D. Marini, and A. Russo. The hitchhiker’s guide to the virtual element method. Mathematical Models and Methods in Applied Sciences, 24(08):1541–1573, 2014.

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