Charlemagne Distinguished Lecture Series - Brezzi
Prof. Dr. Franco Brezzi - Virtual Element Methods
Advanced Numerical Simulation Centre, Istituto Universitario di Studi Superiori (IUSS)
The talk will first (briefly!) recall some basic features of variational formulations, Galerkin approximations, and classical Finite Element Methods applied to some model bondary value problem for Partial Differential Equations.
Then we will present the (brand new!) Virtual Element Method. Roughly speaking the method is a Galerkin method where the finite dimensional subspace is made, locally, of functions (or vector-valued functions) that are solutions of suitable local PDE problems.
As such, the method would be impracticable. As we shall see, the trick consists in being able to compute the local contributions without solving the PDE problems. This can be done with an amount of accuracy that ensures optimal error bounds.
Such an approach allows the use of decompositions where every element may have a very general geometry, instead of being confined to triangles or quadrilaterals (in three dimensions: tetrahedra or hexahedra) as with the classical finite elements