A Fortin Operator for Two-dimensional Taylor-hood Elements

by elements of Taylor-Hood type where Ω is a polygon in R (when triangular elements are considered) or a union of rectangles in R (when rectangular elements are considered). The construction of the Fortin operator will be given in detail for the case of triangular elements. The extension to rectangular elements is discussed briefly in the final section of the paper. More specifically, for triangular elements and k = 2, 3, the velocity vector u is approximated in the space V 0,h = V k h ∩ H0(Ω), where V h is the space of continuous piecewise polynomial vectors of total degree ≤ k and the pressure p is approximated in the space Qk−1 h consisting of continuous piecewise polynomials of total degree ≤ k − 1. The stability of these pairs depends on verification of the classical inf-sup condition