Istituto di Matematica Applicata e Tecnologie Informatiche     
Boffi D., Gastaldi L. On the quadrilateral Q2-P1 element for the Stokes problem. Preprint ercim.cnr.ian//2000-1194, 2000.
The Q2-P1 approximation is one of the most popular Stokes element. Two possible choices are given for the definition of the pressure space: one can either use a global pressure approximation (that is on each quadrilateral the finite element space is spanned by 1 and by the global coordinates x and y) or a local approach (consisting in generating the local space by means of the constants and of the local curvilinear coordinates on each quadrilateral). The former choice is known to provide optimal error estimates on general meshes. This has been shown, as it is standard, by proving a discrete inf-sup condition. In the present paper we check that the latter approach satisfies the inf-sup condition as well. However recent results on quadrilateral finite elements enlight a lack in the approximation properties for the space coming out from the local pressure approach. Numerical results actually show that the second choice (local or mapped pressure approximation) is suboptimally convergent.
Subject Stokes problem, mixed finite elements, quadrilateral

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