Mathematikgebäude, Seminarraum M1011 (10. Etage)

Nonsmooth terms in partial differential equations (PDEs) arise in various applications. Reasons for such nonsmooth terms can, for example, be non-penetration conditions or nonsmooth material laws in continuum mechanics, singular nonlinearities in material science applications, or intrinsic constraints resulting from modeling assumptions.
The numerical treatment of such nonsmooth terms requires special care, because classical nonlinear techniques like, e.g., Newtons method, rely on smoothness. As a consequence such methods typically fail or degenerate for nonsmooth problems making them either inapplicable or inefficient.
In the talk we present a range of numerical methods that have been developed for the numerical treatment of nonsmooth PDEs. A common feature of those methods is, that they rely on convex structure instead of smoothness. The combination of nonsmooth optimization approaches and adaptive multilevel techniques leads to highly efficient and robust methods for nonsmooth or degenerate smooth problems.
The efficiency of the presented numerical methods is illustrated by examples from material science and biomechanics. This is complemented by a discussion on efficient numerical software which is another key ingredient for overall efficiency and an outlook of related current research.

JProf. Dr. Carsten Gräser

Freie Universität Berlin