A uniformly stable Fortin operator for the Taylor-Hood element
The authors construct a new Fortin operator for the lowest order Taylor-Hood element in two space dimensions, which is uniformly stable both in \(L^2\) and \(H^1\). The construction is based on a tight connection between a subspace of the Taylor-Hood velocity space and the lowest order Nedelec edge element. General shape regular triangulations are allowed for the \(H^1\)-stability, while some mesh restrictions are imposed to obtain the \(L^2\)-stability. As a consequence of this construction, a uniform \(\inf\)-\(\sup\) condition associated the corresponding discretizations of a parameter dependent Stokes problem is obtained, and uniform bounds for a family of preconditioners for such problems, without relying on any extra regularity ensured by convexity of the domain can be verified.
scientific article; zbMATH DE number 6141193
scientific article