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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A mixed formulation of Boussinesq equations: Analysis of nonsingular solutions
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by M. Farhloul, S. Nicaise and L. Paquet PDF
Math. Comp. 69 (2000), 965-986 Request permission

Abstract:

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
  • Email: farhlom@umoncton.ca
  • S. Nicaise
  • Affiliation: Université de Valenciennes et du Hainaut Cambrésis, LIMAV, ISTV, B.P. 311, F-59304 - Valenciennes Cedex, France
  • Email: snicaise@univ_valenciennes.fr
  • L. Paquet
  • Affiliation: Université de Valenciennes et du Hainaut Cambrésis, LIMAV, ISTV, B.P. 311, F-59304 - Valenciennes Cedex, France
  • Email: Luc.Paquet@univ_valenciennes.fr
  • Received by editor(s): May 9, 1997
  • Received by editor(s) in revised form: July 15, 1998
  • Published electronically: March 3, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 69 (2000), 965-986
  • MSC (1991): Primary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-00-01186-8
  • MathSciNet review: 1681112