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Stability of higher-order Hood-Taylor methods. (English) Zbl 0731.76042
The stability of a higher-order Hood-Taylor method is proved for the approximation of the velocity and pressure fields in the steady-state Stokes problem with the Dirichlet boundary condition. The original Hood- Taylor method is modified by approximating velocity and pressure fields by using continuous piecewise polynomials of degree 3 and 2 respectively, instead of those of degree 2 and 1. A numerical integration formula which is exact for quadratic polynomials on a triangle is proved. This is then used to establish the modified form of the standard stability condition, which implies that the usual finite element method satisfies a quasi- optimal error estimate.
Reviewer: P.K.Kythe

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
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