Olivier Ricou1, Michel Bercovier2
CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 87-102, 2002, DOI: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.
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