Core Research Areas
Adaptivity for Optimization (AO)
Adaptive techniques are widely used for solving problems involving PDEs, an
there is large agreement that adaptivity in discretizing PDEs is indispensable
constructing efficient algorithms. The study of adaptive techniques for
optimization problems with PDEs is a highly active research area, which is
reflected in several dissertation topics.
Non-Smoothness in Function Spaces (NS)
Many application problems lead to mathematical models with inherent
nonsmooth behavior. This may result from physics itself or from its
mathematical formalization, as for instance in the case of inequality constraints.
The infinite-dimensional nature of all problems involving PDEs requires a proper
treatment of different kinds of nonsmoothness in (infinite-dimensional) function
spaces. This approach allows to identify and analyze the core structure of the
problems and to exploit them for the construction of efficient algorithms.
Interfaces: Separating and Coupling Structures (IS)
Complex models with different physical phenomena on different spatial domains
call for the study of transfer processes across interfaces separating these
domains. The transfer of information across interfaces crucially influences the
behavior of the system. Additionally, the physical system itself can influence the
geometrical location of an interface which leads to moving or free boundary
value problems. In many application settings the interface plays the role of the
design variable resulting in shape optimization or shape identification problems.