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K. Mardal, J. Schöberl, R. Winther:
"A uniformly stable Fortin operator for the Taylor-Hood element";
Numerische Mathematik, 123 (2012), 3; 15 S.

Abstract. A uniform inf{sup condition related to a parameter dependent Stokes problem
is established. Such conditions are intimately connected to the construction of uniform
preconditioners for the problem, i.e., preconditioners which behave uniformly well with
respect to variations in the model parameter as well as the discretization parameter. For
the present model, similar results have been derived before, but only by utilizing extra
regularity ensured by convexity of the domain. The purpose of this paper is to remove
this arti cial assumption. As a byproduct of our analysis, in the two dimensional case we
also construct a new projection operator for the Taylor{Hood element which is uniformly
bounded in L2 and commutes with the divergence operator. This construction is based on
a tight connection between a subspace of the Taylor{Hood velocity space and the lowest
order Nedelec edge element.

http://dx.doi.org/10.1007/s00211-012-0492-6