Local Mass Conservation of Stokes Finite Elements

In this paper we discuss the stability of some Stokes finite elements. In particular, we consider a modification of Hood-Taylor and Bercovier-Pironneau schemes which consists in adding piecewise constant functions to the pressure space. This enhancement, which had been already used in the literature, is driven by the goal of achieving an improved mass conservation at element level. The main result consists in proving the inf-sup condition for the enhanced spaces in a general setting and to present some numerical tests which confirm the stability properties. The improvement in the local mass conservation is shown in a forthcoming paper (Boffi et al. In: Papadrakakis, M., Onate, E., Schrefler, B. (eds.) Coupled Problems 2011. Computational Methods for Coupled Problems in Science and Engineering IV, Cimne, 2011) where the presented schemes are used for the solution of a fluid-structure interaction problem.