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A finite element approximation for the steady solution of a second-grade fluid model

✍ Scribed by Adélia Sequeira; Margarida Baı́a

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
129 KB
Volume
111
Category
Article
ISSN
0377-0427

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✦ Synopsis

The aim of this work is to present a ÿnite element method for the approximation of the steady solution of an incompressible second-grade uid model in two dimensions. The equations for second-grade uids form a system of nonlinear partial di erential equations of mixed elliptic-hyperbolic type (in the steady state). Using a ÿxed-point argument, associated with the decomposition of the system into a transport equation and a Stokes system, existence and uniqueness of the approximate solution are proved and error estimates are obtained. This technique allows the construction of a decoupled ÿxed-point algorithm converging to the discrete solution of the original problem.

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