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The stability of a higher-order Hood–Taylor method for the approximation of the stationary Stokes equations using continuous piecewise polynomials of degree 3 to approximate velocities and continuous piecewise polynomials of degree 2 to approximate the pressure is proved. This result implies that the standard finite element method using these spaces satisfies a quasi-optimal error estimate. The technique used may also be applied to prove the stability of Hood–Taylor rectangular elements of arbitrary degree k for velocities and k - 1 for pressure in each variable.
Brezzi et al. (Sat,) studied this question.