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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