Second-order Elliptic Equations Based On Mixed Finite Element Bubble Functions With Quadratic Elements Simplify The Stabilization Of The Format

In this paper, the simple mixed finite element formats of two degree for the second order elliptic problems, i.e., Possion equations and the plane elastics problems are studied and analyzed , respectively. The mixed finite element formats of the second order element based on bubble fountions , simplified and stabilization, are derived by us. And we give the error estimate.As follows:l.For the Possion equationsFind u, such that,(1)We derive the simplified formats , as follows,(2) For the simplified formats, the error estimate is as follows,Theorem 1. For the finite element space B and M_h,, the problems of mixed finit element have the unique solutions , i.e., the problems of the simplified formats have the unique solutions), and when the generalized solutions of variational problems are the following error estimate holds2 .For the plane elastics problems Find out (σ, u), such that,(l)We derive the simple formats, as follows, Find out such that,(2)For the simplified formats, the error estimate is as follows, Theorem 2. For the finite element space and the problems of mixed finite element have the unique solutions problems of the simplified format have the unique solutions and when the generalized solutions of variational problems are the following error estimate holds...