Research

Former and current research projects:

• Generic software development for grid based methods for solving partial differential equations:
  • parallel, adaptive grid interface (dune-grid module)
  • discretization interface for higher order methods (dune-fem module)
  • generic implementation of base function sets (dune-localfunctions module)

• Numerical methods for non-linear evolution equation
  
  • higher order local timestepping schemes
  • Discontinuous Galerkin and higher order finite-volume schemes for hyperbolic problems
  • Discontinuous Galerkin schemes for elliptic problems
  • Discontinuous Galerkin schemes on moving surfaces
  • parallelisation and local grid adaptation

• Geophysical flow:
  • transparent boundary conditions
  • balancing flux gradients and source terms
  • atmospheric flow
  • free surface water flow

• Radiation-Magnetohydrodynamics:
  • real gas Riemann solvers (energy relaxation method)
  • divergence cleaning (GLM method)
  • numerical schemes (ESC method)
  • convergence analysis

Software projects:

• DUNE - Distributed and Unified Numerics Environment 
• DUNE-FEM - interface and implementation of numerical schemes using DUNE 
• The ALU-Grid Library