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A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions

Authors: M. Farhloul, S. Nicaise and L. Paquet
Journal: Math. Comp. 69 (2000), 965-986
MSC (1991): Primary 65N30
Published electronically: March 3, 2000
MathSciNet review: 1681112
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This paper is concerned with the mixed formulation of the Boussinesq equations in two-dimensional domains and its numerical approximation. The paper deals first with existence and uniqueness results, as well as the description of the regularity of any solution. The problem is then approximated by a mixed finite element method, where the gradient of the velocity and the gradient of the temperature, quantities of practical importance, are introduced as new unknowns. An existence result for the finite element solution and convergence results are proved near a nonsingular solution. Quasi-optimal error estimates are finally presented.

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Additional Information

M. Farhloul
Affiliation: Université de Moncton, Département de Mathématiques et de Statistique, N.B., E1A 3 E9, Moncton, Canada

S. Nicaise
Affiliation: Université de Valenciennes et du Hainaut Cambrésis, LIMAV, ISTV, B.P. 311, F-59304 - Valenciennes Cedex, France

L. Paquet
Affiliation: Université de Valenciennes et du Hainaut Cambrésis, LIMAV, ISTV, B.P. 311, F-59304 - Valenciennes Cedex, France

Received by editor(s): May 9, 1997
Received by editor(s) in revised form: July 15, 1998
Published electronically: March 3, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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