Research Topics

Discontinuous Galerkin Methods

• The LDG method for elliptic problems (with B. Cockburn, I. Perugia, D. Schötzau)
• The LDG method for flow problems (with B. Cockburn, Chr. Schwab, D. Schötzau)
• Strongly divergence free methods for Navier-Stokes equations (with B. Cockburn, D.Schötzau)
• Pointwise a priori anda posteriori estimates for the interior penalty method (with R. Rannacher)
• Coinvestigator in DFG-Schwerpunkt Analysis und Numerik von Erhaltungsgleichungen

Solution Methods and Preconditioners

• Multilevel preconditioning for the interior penalty method and other self-adjoint DG methods (with J. Gopalakrishnan)
• Block preconditioners for the LDG method in saddle point form
• Block preconditioners for DG discretizations of flow problems
• Adaptive projective Newton methods (with H. Hesse)

Scientific Computing

• Finite Element Software deal.II (with W. Bangerth, R. Hartmann)
• Documentation of my own programs (if available) is split into
  1. The application framework
  2. The DG-Shop
  3. The Testsuite
• Parallel methods for radiative transfer

Computational Fluid Dynamics

• Flow with immersed boundaries (with L. Heltai)
• Humidity transfer in electric automotive devices (with Chr. Laux, supported by R. Bosch GmbH)

Radiative Transfer

• Monochromatic radiative transfer in media with varying opacity (linear Boltzmann equation)
• Radiative transfer with Doppler shift in differentially moving media and with partial redistribution (with E. Meinköhn, R. Wehrse)
• Projects supported in grants SFB 359 and SFB 439