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Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity
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SYSNO ASEP 0371221 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Finite element approximation of flow of fluids with shear-rate- and pressure-dependent viscosity Author(s) Hirn, A. (DE)
Lanzendörfer, Martin (UIVT-O) SAI, RID, ORCID
Stebel, Jan (MU-W) RID, ORCID, SAISource Title IMA Journal of Numerical Analysis. - : Oxford University Press - ISSN 0272-4979
Roč. 32, č. 4 (2012), s. 1604-1634Number of pages 31 s. Language eng - English Country GB - United Kingdom Keywords non-Newtonian fluid ; shear-rate- and pressure-dependent viscosity ; finite element method ; error analysis Subject RIV BK - Fluid Dynamics R&D Projects GA201/09/0917 GA ČR - Czech Science Foundation (CSF) IAA100300802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) LC06052 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) AV0Z10190503 - MU-W (2005-2011) UT WOS 000309923300012 EID SCOPUS 84867523146 DOI 10.1093/imanum/drr033 Annotation In this paper we consider a class of incompressible viscous fluids whose viscosity depends on the shear rate and pressure. We deal with isothermal steady flow and analyse the Galerkin discretization of the corresponding equations. We discuss the existence and uniqueness of discrete solutions and their convergence to the solution of the original problem. In particular, we derive a priori error estimates, which provide optimal rates of convergence with respect to the expected regularity of the solution. Finally, we demonstrate the achieved results by numerical experiments. The fluid models under consideration appear in many practical problems, for instance, in elastohydrodynamic lubrication where very high pressures occur. Here we consider shear-thinning fluid models similar to the power-law/Carreau model. A re- stricted sublinear dependence of the viscosity on the pressure is allowed. The mathematical theory concerned with the self-consistency of the governing equations has emerged only recently. We adopt the established theory in the context of discrete approximations. To our knowledge, this is the first analysis of the finite element method for fluids with pressure-dependent viscosity. The derived estimates coincide with the optimal error estimates established recently for Carreau-type models, which are covered as a special case. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
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