Research Interests
Development, analysis and application of finite element methods for partial differential equations
Finite element methods provide a versatile and mathematically well-founded approach to solve partial differential and integral equations arising from mathematical models in physics and engineering. The research activities in this field can be subdivided into:
Development of new algorithms
- hp-adaptive discontinuous Galerkin finite element methods for partial differential equations.
Special attention is given to:
- Space-time discontinuous Galerkin finite element methods in order to deal with moving boundaries and deforming meshes
- Efficient multigrid and (pseudo)-time integration methods to solve the large systems of ordinary differential or nonlinear
algebraic equations resulting from DG discretizations
- Adaptation algorithms controlled by a posteriori error estimates
- Finite element discretizations which preserve important mathematical properties of the
underlying partial differential equations
Special attention is given to:
- Coupled continuous-discontinuous Galerkin finite element methods
- Vector finite elements, such as Whitney elements
- Galerkin least squares finite element methods
Special attention is given to:
- Development of stabilization operators with a solid mathematical background
- Theoretical analysis of finite element methods
Special attention is given to:
- Stability analysis
- A priori error analysis to investigate the optimal rate of convergence
- A posteriori error analysis to control adaptation algorithms
- Applications
Special attention is given to:
- Compressible, incompressible and (dispersed) multiphase flows, including problems with free surfaces
- Maxwell equations
- Development of a general purpose finite element toolkit hpGEM to construct advanced
simulation programs