Park, Chunjae; Sheen, Dongwoo; Shin, Byeong-Chun A subspace of the DSSY nonconforming quadrilateral finite element space for the Stokes equations. (English) Zbl 1311.76070 J. Comput. Appl. Math. 239, 220-230 (2013). Summary: We propose a subspace of the DSSY nonconforming quadrilateral finite element space. The product of this space together with the piecewise constant space can be used for approximating the velocity and pressure variables, respectively, in solving Stokes problems. More precisely, this space consists of the \(P_{1}\)-nonconforming quadrilateral finite element space augmented by macro bubble functions based on the DSSY nonconforming quadrilateral space under a Hood-Taylor type assumption on meshes. It is shown that the pair satisfies the discrete inf-sup condition, using a boundedness estimate of an interpolation operator based on edge integrals. Numerical results are presented. Cited in 5 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:quadrilateral nonconforming finite elements; inf-sup condition; boundedness of interpolation PDFBibTeX XMLCite \textit{C. Park} et al., J. Comput. Appl. Math. 239, 220--230 (2013; Zbl 1311.76070) Full Text: DOI