Finite Elements with Local Projection Stabilization for Incompressible Flow Problems

Braack, Malte and Lube, G. (2009) Finite Elements with Local Projection Stabilization for Incompressible Flow Problems Journal of Computational Mathematics, 27 (2-3). pp. 116-147.

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Abstract

In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization (LPS). These methods preserve the favourable stability and approximation properties of classical residual-based stabilization (RBS) techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the Navier-Stokes equations. Furthermore, we apply it to optimal control problems with linear(ized) How problems, since the symmetry of the stabilization leads to the nice feature that the operations "discretize" and "optimize" commute.

Document Type: Article
Keywords: finite element methodstabilization; computational fluid dynamics; error estimates navier-stokes; stokes; navier-stokes equations; partial-differential-equations; variational multiscale method; computational fluid-dynamics; system least-squares; oseen problem; formulation
Research affiliation: Kiel University
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
ISSN: 0254-9409
Projects: Future Ocean
Date Deposited: 11 Feb 2011 12:14
Last Modified: 04 Jul 2017 09:41
URI: http://eprints.uni-kiel.de/id/eprint/9311

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