Approximation of the Steklov problem on a non Lipschitz domain

LOMBARDI, ARIEL L.

Pavia

Conferencia; Seminario del Istituto di Matematica Applicata e Tecnologie Informatiche; 2018

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.