# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Priv.-Doz. Dr. Johannes
Kraus**, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences (ÖAW),
will give a public talk (followed by a discussion) on **Fri, July 3, 2009**
at **08:00 o'clock** at **HF 9905**
on the topic of
"Algebraic multilevel methods for elliptic finite element equations"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Algebraic multilevel methods for elliptic finite element equations

In this talk algebraic multilevel iteration (AMLI) methods for solving elliptic finite element equations with symmetric positive definite (SPD) matrices are discussed. After a short introduction to finite element methods, we describe linear and nonlinear AMLI algorithms, comment on their computational complexity and recall classical convergence results.

Next we present some recent developments in extending the theory of AMLI methods to nonconforming finite element discretizations including discrete problems arising from interior penalty (IP) discontinuous Galerkin (DG) formulations. A key issue in all cases - classes of problems - under consideration is the robustness of the preconditioner with respect to certain problem parameters. We give several examples of constructing optimal order methods for nearly singular systems, also for vector-field problems such as linear elasticity systems, or variational problems in H(div).

Finally we point out the relation between AMLI and (classical) algebraic multigrid (AMG) methods.