Theoretical aspects of coupling of function theoretic methods and finite element method

Presenter: Dmitrii Legatiuk, Bauhaus-Universität Weimar, Germany

Joint work with Klaus Gürlebeck

The purpose of this talk is to present important steps in a process of coupling of an analytical solution with the finite element method. Based on previous results we summarize a theory of such coupling. We present the goal of the coupling, and we describe the procedure which assures a continuous coupling between two solutions. Finally, we show results about the convergence of the proposed mixed scheme. We start by developing a theory for two-dimensional problems of linear elastic fracture mechanics, and in the end we present a concept for a generalisation of the proposed method to spatial problems.