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Pointwise Accuracy of a Stable Petrov-Galerkin Approximation to the Stokes Problem

Ricardo G. Duran and Ricardo H. Nochetto
SIAM Journal on Numerical Analysis
Vol. 26, No. 6 (Dec., 1989), pp. 1395-1406
Stable URL: http://www.jstor.org/stable/2157746
Page Count: 12
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Pointwise Accuracy of a Stable Petrov-Galerkin Approximation to the Stokes Problem
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Abstract

The finite-element approximation of the Stokes problem due to Hughes, Franca, and Balestra [Comput. Meth. Appl. Mech. Engrg., 59 (1986), pp. 85-99] is analyzed in maximum norm. The method consists of modifying the usual bilinear form associated with the saddle-point structure to become coercive over the finite-element space. Exploiting the enhanced stability--thus getting rid of the inf-sup condition--yields quasi-optimal L∞-error estimates for both velocity and pressure.

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