Mixed Finite Element Methods For 4th Order Elliptic Equations

In this paper, we focus on the study of the mixed finite element schemes for 4th order elliptic problem. Some new mixed finite element schemes are presentd based on two different variational formulars. The convergences of these elements are proved and the error estimates are given.At first, we generalize the various results about the mixed finite element scheme for solving 4th order elliptic equations and study the relationship between them. Next, we give two mixed finite element schemes based on known C~1-elements. Finally, we give a new method for the numerical approximation of the biharmonic problem. This method is based on the mixed method given by Ciarlet-Raviart. We have an error estimate result which is better than before.