The Mathematical Institute, University of Oxford, Eprints Archive

Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology

Diening, Lars and Kreuzer, Christian and Suli, Endre (2012) Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology. Technical Report. SINUM. (Submitted)

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Abstract

We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multi–valued, maximal monotone $r$-graph, with $1 < r < \infty$. Using a variety of weak compactness techniques, including Chacon’s biting lemma and Young measures, we show that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to 0. A key new technical tool in our analysis is a finite element counterpart of the Acerbi–Fusco Lipschitz truncation of Sobolev functions.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Partial differential equations
D - G > Fluid mechanics
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1509
Deposited By:Lotti Ekert
Deposited On:14 Apr 2012 09:06
Last Modified:14 Apr 2012 09:06

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