Giovedì 29 Novembre 2018, alle ore 15 precise, presso la sala conferenze dell’IMATI-CNR di Pavia, il

Dr. Ariel Lombardi, Universidad Nacional de Rosario y CONICET, Argentina

terrà un seminario dal titolo:

Finite element Approximation of the Steklov problem posed in a non Lipschitz domain

nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia),

http://matematica.unipv.it/it/seminari-matematica-applicata

Al termine della conferenza sarà organizzato un piccolo rinfresco.

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Abstract.
In this talk, first we will review some results concerning the finite element approximation of a simple Neumann problem for the Laplace operator on a non Lipschitz domain with an external cusp. The difficulties in our analysis come from the fact that some trace inequalities and extension theorems are not valid for that kind of domain. These difficulties can be overcome and almost optimal-convergence is proved for the piecewise linear approximation. Then we will consider the Steklov problem on the same domains for which we obtain a convergence result for the numerical approximation with linear finite elements. Numerical experiments suggest that our result is not optimal for all the cases, but, in principle, it assures the minimal possible order of convergence.