Error analysis of some finite element methods for the Stokes problem

Stenberg, Rolf

doi:10.1090/S0025-5718-1990-1010601-X

Error analysis of some finite element methods for the Stokes problem
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Math. Comp. 54 (1990), 495-508 Request permission

Abstract:

We prove the optimal order of convergence for some two-dimensional finite element methods for the Stokes equations. First we consider methods of the Taylor-Hood type: the triangular ${P_3} - {P_2}$ element and the ${Q_k} - {Q_{k - 1}},$, $k \geq 2$, family of quadrilateral elements. Then we introduce two new low-order methods with piecewise constant approximations for the pressure. The analysis is performed using our macroelement technique, which is reviewed in a slightly altered form.

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