Discontinuous Galerkin methods for conservation and balance laws, in particular for the Euler equations, the Navier-Stokes equations and the shallow water equations
Numerical methods for fluid-structure-interaction
Positivity preserving time integration methods
High order, conservative space discretization methods using summation-by-parts operators
IMEX and multirate time integration
Efficient shock capturing methods for DG schemes
Application of image processing techniques to numerical solutions as a postprocessing routine to filter out remaining oscillations in the vicinity of shocks
