Quasi-optimality of nonconforming methods for linear variational problems

Pietro Zanotti

Universita' degli Studi di Milano

Thursday 16th March 2017

11:00:00

Aula Seminari "Saleri" VI Piano MOX-Dipartimento di Matematica, Edificio 14 POLITECNICO DI MILANO

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