A Nonconforming Finite Element For The Three Dimensional Stokes Problem

Stokes problem is one kind of important problem in hydromechanics, and a standard mixed problem, in which the speed and the pressure are computated at the same time .For stokes problem the most important point is that the element must satisfy the discrete Babuska-Brezzi condition. The Hood-Taylor conforming finite element approaching method has been considered by Hood-Taylor, The famous Crouzeix-Raviart nonconforming finite element has been suggested by Crouzeix-Raviart,which has one-order convergence rate. Because of bilinear and linear elements do not satisfy discrete B-B condition ,the two elements are improved by using the macro element method or adding the bubble funtion by Girault-Raviart and Brezzi-Fortin,but analysis process is rather trouble.In this paper we based on the the characteristics of convergence of nonconforming finite element method , focused on mixed finite element approach for three-dimensional Stokes problem, we constructure a tetrahedral finite element.We prove that this element satisfies the discrete B-B condition,the discrete system is uniquely solvable,and the convergence rates for the velocity and pressure are order two.