Stabilized Finite Element Methods for the Oberbeck–Boussinesq Model

Helene Dallmann; Daniel Arndt

doi:10.1007/s10915-016-0191-z

Stabilized Finite Element Methods for the Oberbeck–Boussinesq Model

Helene Dallmann, Daniel Arndt

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	244-273
Number of pages	30
Journal	Journal of Scientific Computing
Volume	69
Issue number	1
DOIs	https://doi.org/10.1007/s10915-016-0191-z
State	Published - Oct 1 2016
Externally published	Yes

Funding

The second author was supported by CRC 963 founded by German research council (DFG).

Funders	Funder number
Deutsche Forschungsgemeinschaft

Keywords

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

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10.1007/s10915-016-0191-z

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abstract = "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.",

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

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AU - Arndt, Daniel

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N2 - 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.

AB - 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.

KW - Grad-div stabilization

KW - Local projection stabilization

KW - Navier–Stokes equations

KW - Non-isothermal flow

KW - Oberbeck–Boussinesq model

KW - Stabilized finite elements

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JF - Journal of Scientific Computing

IS - 1

ER -

Stabilized Finite Element Methods for the Oberbeck–Boussinesq Model

Abstract

Funding

Keywords

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