A kind of full-discrete nonconforming finite element method is proposed for the parabolic variational inequality.

By using the spectrum approximation theory of compact operator, the approximation of anisotropic nonconforming ?nite element method for Stokes eigenvalue pronlem are presented and the optimal error estimates are obtained, which are as same as those of traditional ?nite element methods.

Using the method of analysing Specht element, the application of nonconforming arbitrary quadrilateral element to the unilateral problem is studied, and the convergence analysis and optimal error estimates are given.

Investigation of internal parameter type incompatible elements with rotational degrees of freedom;

Contra-solution of solving displacement basic formulae of incompatible element;

Annotation about inner degrees of freedom of incompatible element;

By using nonconforming element and Bramble-Hilbert-Xu Lemma, Laplace approximating eigenvalue is given by the means of asymptotic expansion and the main error terms are presented ,too.

We expand eigenvalue of possion equqtion using Q1rot nonconforming element.

The domain decomposition method for the lowest order Raviart Thomas triangular mixed element method and projection nonconforming element method with non quasi uniform partition is given for nonselfadjoint and indefinite second order elliptic problem under minimal regularity assumption,meanwhile an optimal convergence rate is obtained for GMRES method.

The second order elliptic problem is studied by using conforming finite element and nonconforming finite element in the different parts of the area respectively.

The paper mainly discussed finite element methods for a Navier-Stokes equation and a class of rectangular nonconforming finite element was presented that can be applied.

By using the special properties of the elementt,he optimal error estimates are obtained,which extends the application scope of nonconforming finite element.