Volume 27, Issue 2-3
Finite Elements with Local Projection Stabilization for Incompressible Flow Problems

Malte Braack & Gert Lube

DOI:

J. Comp. Math., 27 (2009), pp. 116-147.

Published online: 2009-04

Preview Full PDF 65 1429
Export citation
  • Abstract

In this paper we review recent developments in the analysis of finite elementmethods for incompressible flow problems with local projection stabilization(LPS). These methods preserve the favourable stability and approximationproperties of classical residual-based stabilization (RBS) techniques but avoidthe strong coupling of velocity and pressure in the stabilizationterms. LPS-methods belong to the class of symmetric stabilization techniquesand may be characterized as variational multiscale methods. In this workwe summarize the most important a priori estimates of thisclass of stabilization schemes developed in the past 6 years.We consider the Stokes equations, the Oseen linearizationand the Navier-Stokes equations. Furthermore, we apply it tooptimal control problems with linear(ized) flow problems, since thesymmetry of the stabilization leads to the nice featurethat the operations "discretize" and"optimize" commute.

  • Keywords

Finite element method Stabilization Computational fluid dynamics Error estimates Navier-Stokes Stokes

  • AMS Subject Headings

65N06 65B99.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-27-116, author = {}, title = {Finite Elements with Local Projection Stabilization for Incompressible Flow Problems}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {116--147}, abstract = {

In this paper we review recent developments in the analysis of finite elementmethods for incompressible flow problems with local projection stabilization(LPS). These methods preserve the favourable stability and approximationproperties of classical residual-based stabilization (RBS) techniques but avoidthe strong coupling of velocity and pressure in the stabilizationterms. LPS-methods belong to the class of symmetric stabilization techniquesand may be characterized as variational multiscale methods. In this workwe summarize the most important a priori estimates of thisclass of stabilization schemes developed in the past 6 years.We consider the Stokes equations, the Oseen linearizationand the Navier-Stokes equations. Furthermore, we apply it tooptimal control problems with linear(ized) flow problems, since thesymmetry of the stabilization leads to the nice featurethat the operations "discretize" and"optimize" commute.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8564.html} }
TY - JOUR T1 - Finite Elements with Local Projection Stabilization for Incompressible Flow Problems JO - Journal of Computational Mathematics VL - 2-3 SP - 116 EP - 147 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8564.html KW - Finite element method KW - Stabilization KW - Computational fluid dynamics KW - Error estimates KW - Navier-Stokes KW - Stokes AB -

In this paper we review recent developments in the analysis of finite elementmethods for incompressible flow problems with local projection stabilization(LPS). These methods preserve the favourable stability and approximationproperties of classical residual-based stabilization (RBS) techniques but avoidthe strong coupling of velocity and pressure in the stabilizationterms. LPS-methods belong to the class of symmetric stabilization techniquesand may be characterized as variational multiscale methods. In this workwe summarize the most important a priori estimates of thisclass of stabilization schemes developed in the past 6 years.We consider the Stokes equations, the Oseen linearizationand the Navier-Stokes equations. Furthermore, we apply it tooptimal control problems with linear(ized) flow problems, since thesymmetry of the stabilization leads to the nice featurethat the operations "discretize" and"optimize" commute.

Malte Braack & Gert Lube. (2019). Finite Elements with Local Projection Stabilization for Incompressible Flow Problems. Journal of Computational Mathematics. 27 (2-3). 116-147. doi:
Copy to clipboard
The citation has been copied to your clipboard