Tuesday, 29 November 2018, 3 p.m. (sharp),

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

at the conference room of IMATI-CNR in Pavia, will give a lecture titled:

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

as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).

At the end a refreshment will be organized.


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.