Open Access

ARTICLE

A dimensional reduction of the Stokes problem

Olivier Ricou¹, Michel Bercovier²
1 Laboratoire d’Analyse Numérique, Tour 55-56, 5^e étage, Université Pierre & Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05. E-mail: ricou@ann.jussieu.fr
2 Institute of Computer Science, The Hebrew University, Jerusalem 91904, Israel (on leave at DER Falcult Lonard de Vinci, Paris la Dfense, France). E-mail: berco@cs.huji.ac.il

Computer Modeling in Engineering & Sciences 2002, 3(1), 87-102. https://doi.org/10.3970/cmes.2002.003.087

Abstract

In this article, we present a method of reduction of the dimension of the Stokes equations by one in a quasi-cylindrical domain. It takes the special shape of the domain into account by the use of a projection onto a space of polynomials defined over the thickness. The polynomials are defined to fit as well as possible with the variables they approximate. Hence, this method restricted to the first polynomial, recovers the Hele-Shaw approximation.
The convergence of the approximate solution to the continuous one is shown. Under a regularity hypothesis, we also obtain error estimates.
A description of the stiffness matrix is exhibited and some computations show the acceleration due to this method. Finally a few numerical results are given.

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Keywords

dimentionnal reduction, Stokes, Hele-Shaw

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