Scientific Computing on polytopes & Deeper into Virtual Element Methods

SpeakerFranco Brezzi

Professor of Istituto Universitario di Studi Superiori (IUSS) Italy Vice President of the European Mathematical Society

Date & Time10:00-12:10, Dec.16, 2016

LocationM842, Lecture Hall, Beijing Institute for Scientific and Engineering Computing, 8th Floor, Scientific Research Building

About the speaker:

Franco Brezzi works on the theoretical bases of Scientific Computing, in particular in Numerical Methods for Partial Differential Equations, where he hasmade fundamental contributions to Mixed Finite Element Methods, Mimetic Finite Differences, or Virtual Elements of problems related to Structural Mechanics, Fluid Mechanics, and Electro-Magnetics,including algorithms and theories. He was awarded the Gauss-Newton gold medal of the International Association for Computational Mechanics of the World Congress of Computational Mechanics in 2004,SIAM von Neumann award in 2009,and the Leonhard Euler Medal and the Ritz-Galerkin Medalof the European Community on Computational Methods in Applied Science in 2014 and 2016, respectively.

Talk 1: 10:00-10:50, Dec. 16, 2016

Title: Scientific Computing on polytopes

AbstractAfter a brief recalling on variational formulations and Galerkin approximations, we will discuss advantages and difficulties related to approximations based on a decomposition of the computational domain into elements of a rather general shape (polygons and polyhedrons). We will briefly overview some of the more recent methodologies, and then concentrate more on the general aspects of Virtual Element Methods.

Talk 2: 11:20-12:10, Dec. 16, 2016

Title: Deeper into Virtual Element Methods

AbstractWe will continue the discussion on Virtual Element Methods, entering more specialized aspects as the Serendipity reduction, the discretization of Vector Valued functional spaces (H(curl) and H(div)-conforming), the construction of discrete L2-inner products for VEM spaces, and their use in the discretization of PDEs.