Higher order isoparametric finite element solution of Stokes flow

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Date

2005

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Elsevier Science inc

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

A finite element method of the penalization type, using higher order shape functions with rectangular elements, is presented for the solution of the Stokes flow. The fluid is viscous and the flow is slow, steady and incompressible. The solution has been obtained in terms of velocity field while the pressure terms are eliminated using the penalty function approach. The degree of the finite element approximation can be increased as much as one needs with this higher order shape function formulation. The method is tested in a lid-driven square cavity and it is found that there is a relationship between the viscosity and penalty parameter. From one solution one can obtain all the other solutions only by arranging one of the parameters since the product of these parameters has been shown that is a fixed constant. Selected graphs of the velocity field are given showing these behaviors. (C) 2004 Elsevier Inc. All rights reserved.

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Keywords

higher order isoparametric, finite element method, Stokes flow

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Citation

5

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Volume

162

Issue

3

Start Page

1083

End Page

1101

URI

https://doi.org/10.1016/j.amc.2004.01.014
 https://hdl.handle.net/20.500.14411/1237

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