A Stabilized Nonconforming Quadrilateral Finite Element Method for the Generalized Stokes Equations

Abstract

In this paper, we study a local stabilized nonconforming finite element method for the generalized Stokes equations. This nonconforming method is based on two local Gauss integrals, and uses the equal order pairs of mixed finite elements on quadrilaterals. Optimal order error estimates are obtained for velocity and pressure. Numerical experiments performed agree with the theoretical results.