Stabilized Finite Element Methods for the Oberbeck---Boussinesq Model
2016
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.
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