Stability of Higher-Order Hood–Taylor Methods

Abstract

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.