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 L 2 can be established, as well as one in a broken H 1-norm for the velocity.
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Received: January 1999 / Accepted: April 1999
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Cai, Z., Douglas, J. & Ye, X. A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations. CALCOLO 36, 215–232 (1999). https://doi.org/10.1007/s100920050031
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DOI: https://doi.org/10.1007/s100920050031