# A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations

@article{Cai1999ASN, title={A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations}, author={Zhiqiang Cai and Jim Douglas and Xiu Ye}, journal={CALCOLO}, year={1999}, volume={36}, pages={215-232} }

Abstract:Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier–Stokes equations, along with a piecewise-constant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for the approximation of both the velocity and pressure in L2 can be established, as well as one…

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