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IMA Journal of Numerical Analysis 2001 21(1):143-164; doi:10.1093/imanum/21.1.143
© 2001 by Institute of Mathematics and its Applications
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Mixed finite element analysis of a non-linear three-fields Stokes model

H. Manouzi1 and M. Farhloul2

1 Département de Mathématiques et de Statistique, Université Laval, Québec, G1K7P4, Canada 2 Département de Mathématiques et de Statistique, Université de Moncton, Moncton, NB, E1A 3E9, Canada

In this article, a mixed finite element analysis of the non-linear Stokes problem with monotone constitutive laws is considered. We construct a new three-field model for incompressible fluids where the velocity u, the non-linear stress tensor {sigma} = {Psi} (|{nabla}u|) {nabla}u and the pressure p are the most relevant unknowns. We give existence and unicity results for the continuous problem and its approximation. Stable and optimal error estimates under minimal regularity assumptions are derived and numerical results are presented.

Received 29 April 1999. Accepted 30 November 1999.


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