An Inf-Sup Stabilized Finite Element Method by Multiscale Functions for the Stokes Equations (Advances in Applied Mathematics and Mechanics, 2018)
In the paper, an inf-sup stabilized finite element method by multiscalefunctions for the Stokes equations is discussed. The key idea is to use a Petrov-Galerkin approach based on the enrichment of the standard polynomial space forthe velocity component with multiscale functions. The inf-sup condition for $P_1$-$P_0$ triangular element (or $Q_1$-$P_0$ quadrilateral element) is established. And the optimalerror estimates of the stabilized finite element method for the Stokes equationsare obtained.