A Stabilized Method Of P2-P1 Element And P2-P2 Element For There-dimensional Stokes Equations

A low order stabilized mixed element for the two-dimensional Stokes equations, there has been some research results.In this paper, we study the three-dimensional Stokes equations and devoted primarily to the stabilisation of mixed finite element methods.Under the general mesh the finite element space P2-P1 combination for the velocity and pressure for the Stokes equa-tions does not satisfy inf-sup condition.We will apply local inf-sup condition to obtain the inf-sup stability condion that is essential to finite elements approximation of Stokes problem.Then,a sta-bilisation procedure for mixed finite element methods is presented.With the stability theory,we obtain the stabilisation and error estimates of the P2-P2 element for the Stokes equations of three-dimensional.