The cascadic multigrid method for the second order elliptic problem is considered, which is discretized by P1 nonconforming element, or Carey element, or Wilson element, is accurate and has the optimal complexity.

The congvergence analysis for the second order hyperbolic equation with the P1-nonconforming finite element is discussed.

In this paper,convergence analysis of the modified P1-nonconforming finite element for the viscoelasticity equation is discussed.

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.