• Adaptivity, (stochastic) FEM and FVM, moving and anisotropic meshes
• A posteriori error estimation and global error control
• Linearly implicit time integrators for stiff problems
• Adaptive large eddy simulation in reactive flows
• Optimal control with PDEs
• Modelling, simulation and optimization of water/gas networks
• Uncertainty quantication with random PDEs
• Model order reduction

• 25th Biennial Numerical Analysis Conference, Glasgow, 25-28 June 2013
• ENUMATH 2013, European Numerical Mathematics and Advanced Applications, Lausanne, August 26-30, 2013
• SciCADE 2013, the International Conference on Scientific Computation and Differential Equations, Valladolid, September 16-20, 2013
• 26th Chemnitz FEM Symposium, Chemnitz, 23-25 September 2013
• ECMI 2014, the 18th European Conference on Mathematics for Industry, Taormina, 9-13 June 2014
• WCCM XI, 11th World Congress on Computational Mechanics, Barcelona, 20-25 July 2014

Editor of the Journal Applied Numerical Mathematics

• Center of Smart Interfaces: Understanding and Designing Fluid Boundaries (CSI), Excellence Initiative of the federal government of Germany.
  
  
  

• Adaptive multilevel SQP-methods for PDAE-constrained optimization with restrictions on control and state
  DFG, Optimization with PDEs (SPP 1253), 2009-2012, joint project with S. Ulbrich (Darmstadt)

• Adaptive higher order time integrators for LES Project in DFG-Graduate College "Instationary system modelling for aircraft turbines" at TU Darmstadt, 2006-2014

• Large eddy simulation with adaptive moving meshes for the solution of meteorological problems
  DFG, Metstroem (SPP 1276), 2007-2013, joint project with J. Fröhlich (Dresden) and A. Dörnbrack (DLR Oberpfaffenhofen)