Brezzi, Franco; Falk, Richard S. Stability of higher-order Hood-Taylor methods. (English) Zbl 0731.76042 SIAM J. Numer. Anal. 28, No. 3, 581-590 (1991). 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 Cited in 73 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76D07 Stokes and related (Oseen, etc.) flows Keywords:stability; higher-order Hood-Taylor method; steady-state Stokes problem; finite element method PDFBibTeX XMLCite \textit{F. Brezzi} and \textit{R. S. Falk}, SIAM J. Numer. Anal. 28, No. 3, 581--590 (1991; Zbl 0731.76042) Full Text: DOI