Mathematikgebäude, Seminarraum M614/616 (6. Etage)

It is well known that standard Galerkin methods on equidistant meshes and even on layer adapted meshes lead to oscillations in the solution. Using stabilised methods, these oscillations can be reduced. One of these techniques is the discontinuous Galerkin method that uses discontinuous elements instead of continuous ones and allows jumps across inner edges. A drawback is the much higher number of degrees of freedom and therefore a much higher computational cost.
We investigate the use of reduced dG methods, where continuous elements are enriched by some discontinuous bubble functions of higher degree. Hereby the stability of the method is increased but less degrees of freedom compared with the full discontinuous Galerkin method are used.
This approach follows a series of papers by M. Bittl, D. Kuzmin and R. Becker.

PD Dr. Sebastian Franz

TU Dresden