Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows

  • Gert Lube
  • Daniel Arndt
  • Helene Dallmann
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 108)


The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.


Stokes Problem Subgrid Model Fluctuation Operator Oseen Problem Local Mass Conservation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work of Daniel Arndt was supported by CRC 963 founded by German research council (DFG). The work of Helene Dallmann was supported by the RTG 1023 founded by German research council (DFG).


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for Numerical and Applied MathematicsUniversity of GöttingenGöttingenGermany

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