Journal of Scientific Computing

, Volume 69, Issue 1, pp 244–273

Stabilized Finite Element Methods for the Oberbeck–Boussinesq Model


DOI: 10.1007/s10915-016-0191-z

Cite this article as:
Dallmann, H. & Arndt, D. J Sci Comput (2016) 69: 244. doi:10.1007/s10915-016-0191-z


We consider conforming finite element approximations for the time-dependent Oberbeck–Boussinesq model with inf-sup stable pairs for velocity and pressure and use a stabilization of the incompressibility constraint. In case of dominant convection, a local projection stabilization method in streamline direction is considered both for velocity and temperature. For the arising nonlinear semi-discrete problem, a stability and convergence analysis is given that does not rely on a mesh width restriction. Numerical experiments validate a suitable parameter choice within the bounds of the theoretical results.


Oberbeck–Boussinesq model Navier–Stokes equations Stabilized finite elements Local projection stabilization Grad-div stabilization Non-isothermal flow 

Mathematics Subject Classification

65M12 65M60 76D05 

Funding information

Funder NameGrant NumberFunding Note
Deutsche Forschungsgemeinschaft (DE)
  • RTG 1023
Deutsche Forschungsgemeinschaft (DE)
  • CRC 963

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute for Numerical and Applied MathematicsGeorg-August University of GöttingenGöttingenGermany

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