Finite element approximation of fractional diffusion

Friday, July 12th 12:00-13:00, 2019
Logistar Room at DeustoTech, University of Deusto.

Juan Pablo Borthagaray
University of Maryland, USA and Universidad de la República, Uruguay

We approximate the integral formulation of the fractional Laplacian in bounded polyhedral domains. We discuss how to deal numerically with the singular non-integrable kernel, derive optimal energy estimates, and discuss preconditioning with emphasis on the boundary behavior and how to cope with the reduced boundary Sobolev regularity. We further examinefractional obstacle problems and fractional minimal graphs in light of the newly developed linear theory, with emphasis on the development of boundary discontinuities.