Habilitationskolloqium "High order FEM-fast solvers for tensor product elements"
Priv.-Doz. Dr. Sven BeuchlerOct. 9, 2008, 1 p.m. HF 136
In this talk, the discretization of elliptic boundary value problems by means of the hp-version of the ﬁnite element method is considered. The presentation starts with a motivation for high order ﬁnite elements. In the main part of the talk, we will focus on the eﬃcient solution of the system of linear algebraic equations. The solution of the system is performed by the preconditioned conjugate gradient method in almost optimal arithmetical complexity where the preconditioners exploit the tensor product structure of the elements. Several numerical examples show the eﬃciency of the proposed solvers. Finally, a solver for an interface concentrated ﬁnite element discretization is presented.
The presented results are collaborations with D. Braess (Bochum), T. Eibner (Chemnitz), U. Langer, R. Schneider (Berlin), and C. Schwab (Zürich).