Published

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

Long Chen

Computers and Mathematics with Applications. 68(10), 1368-1373, 2014

pdf   Bibtex

ABSTRACT:

 A Fortin operator is constructed to verify the discrete
inf-sup condition for $P^2_0-P^1$ Taylor-Hood element and its variant
$P^2_0-(P^1 + P_0)$ in two dimensions. The approach is closely related
to the recent work by Mardal, Schoberl and Winther
(Numer. Math. 2012). 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 for $P^2_0-P^1$ element is uniformly bounded in both $H^1$
and $L^2$ norm for general shape regular triangulations.