Welcome to the Chair of Numerical Mathematics
Prof. Dr. Markus Bause
Numerical simulations of time dependent physical, biological and chemical processes are desirable in several fields of natural sciences and a large number of branches of engineering. The ability to simulate complex, coupled and multiscale phenomena with high efficiency and reliability is particularly important from the point of view of physical realism. It continues to remain a challenging task.
The group of Numerical Mathematics conducts research in the design and numerical analysis of finite element based approximation schemes for partial differential equations and their implementation in a parallel software platform for three-dimensional computations of high resolution in space and time.
The research focuses on:
- Space-time finite element methods
- Discontinuous and mixed finite element methods
- A posteriori error control and adaptivity in space and time
- Stabilization techniques for convection-dominated transport
- Monolithic solver
- Techniques of preconditioning
Fields of applications are:
- Elastic and acoustic wave propagation
- Incompressible and compressible fluid flow
- Multicomponent reactive transport
- Fluid-structure interaction
- Sophisticated problems of multiphysics
Parallel implementations of the schemes are done in the group’s frontend software DTM++ to the deal.II library and the Trilinos project.
For the students the group develops and offers preparatory courses in mathematics in German and English language. The courses are implemented in a software platform based on the learning management system ILIAS and the computer algebra system Maxima.