Seminars

Quasi-optimality of nonconforming methods for linear variational problems

Speaker: Pietro Zanotti
Affiliation: Universita' degli Studi di Milano
When: Thursday 16th March 2017
Time: 11:00:00
Abstract: We consider the approximation of linear elliptic variational problems, symmetric for simplicity. According to the Cea's lemma, conforming Galerkin methods for these problems are quasi-optimal. Conversely, a simple argument reveals that classical nonconforming methods do not enjoy such property. Motivated by this observation, we derive necessary and sufficient conditions for quasi-optimality, within a large class of methods. Moreover, we identify the quasi-optimality constant and discuss its ingredients. In the second part of the talk, we present a detailed construction of two quasi-optimal nonconforming methods for a model problem and show that the corresponding quasi-optimality constants are bounded in terms of the shape parameter of the underlying meshes. This is a joint work with Andreas Veeser. contact: paola.antonietti@polimi.it simona.perotto@polimi.it