Analysis and stabilisation methods for singularly perturbed problems and systems

• Applicant: Privatdozent Dr. Sebastian Franz
• Subject Area: Mathematics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 220991365

When singularly perturbed problems are solved numerically on a uniform mesh with standard methods, the numerical solution often exhibits spurious oscillations. On the other hand, if stabilised methods and layer-adapted meshes are used, the exact solutions are well approximated.For relatively simple problems like convection diffusion in the unit square the behaviour of solutions and the construction of layer adapted meshes is well understood. For more complex problems like the Oseen equations, this is an open question. Thus, a main goal of this proposal is to investigate the solution behaviour of problems like the Oseen-equations together with suitable stabilisation methods. This is an important milestone to a better understanding of the solution behaviour of Navier-Stokes equations.

• DFG Programme: Research Grants