Divergence-free Mixed Finite Elements for the incompressible Navier-Stokes equations

December 8, 2009

Time: December 8, 2009
Lecturer: Dr. Alexander Linke
Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin
Venue: Pfaffenwaldring 61, Raum U1.003 (MML), Universität Stuttgart
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Mixed finite elements are a classical approach for the discretizationof the incompressible Navier-Stokes equations. With different spaces forthe velocity and the pressure, a large class of convergent methods canbe designed. But the quality of the obtained discretization dependsstrongly on the chosen pair of velocity-pressure spaces. A badcombination of these two spaces leads to the occurrence of differentkinds of spurious oscillations in the discrete pressure or in thediscrete velocity. In the talk, the impact of spurious oscillations dueto weak mass conservation will be investigated, and the divergence-freeScott-Vogelius element will be presented. Further, the impact of weakmass conservation in coupled problems will be treated.
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