A simple construction of a Fortin operator for the two dimensional Taylor–Hood element

A Fortin operator is constructed to verify the discrete inf–sup condition for the lowest order Taylor–Hood element and its variant in two dimensions. The approach is closely related to the recent work by Mardal et al. (2013). That is based on the isomorphism of the tangential edge bubble function space to a subspace of the lowest order edge element space. A more precise characterization of this subspace and a numerical quadrature are introduced to simplify the analysis and remove the mesh restriction. The constructed Fortin operator is stable in both H1H1 and L2L2 norm for general shape regular triangulations.