Knobloch, Petr; Tobiska, Lutz Modified FE discretizations of incompressible flow problems and their relationship to stabilized methods. (English) Zbl 1006.76057 Neittaanmäki, Pekka (ed.) et al., ENUMATH 99. Numerical mathematics and advanced applications. Proceedings of the 3rd European conference, Jyväskylä, Finland, July 26-30, 1999. Singapore: World Scientific. 571-578 (2000). Summary: We consider conforming finite element discretizations of two-dimensional stationary incompressible Stokes and Navier-Stokes equations based on triangular and quadrilateral meshes. We present a general approach for interpreting stabilized methods as modified Galerkin discretizations employing bubble functions. This interpretation provides a deeper insight into the behaviour of stabilized methods, and is a valuable tool for their theoretical investigations. Further, we show how new types of stabilizations can be derived.For the entire collection see [Zbl 0954.00041]. Cited in 1 Document MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 76D07 Stokes and related (Oseen, etc.) flows Keywords:conforming finite element discretizations; Navier-Stokes equations; quadrilateral meshes; stabilized methods; modified Galerkin discretizations; bubble functions PDFBibTeX XMLCite \textit{P. Knobloch} and \textit{L. Tobiska}, in: ENUMATH 99. Numerical mathematics and advanced applications. Proceedings of the 3rd European conference, Jyväskylä, Finland, July 26--30, 1999. Singapore: World Scientific. 571--578 (2000; Zbl 1006.76057)