Elliptic Boundary Value Problems For Nonconforming Finite Element Analysis, Multi-grid Method

In this paper,we first focus on the multigrid method of nonconforming finite element for 2nd order elliptic problem.A universal convergence theorem was given, which can be easily applied to the analysis and construction of transfer operator for the multigrid method of nonconforming finite element, we define the transfer operator of 3-D Wilson element and prove the convergence of the element by using the convergence theorem we given.Then,we conside the multigrid method of nonconforming finite element for 4nd order elliptic problem.we apply double set parameter method to Morley element and construct a new ele-ment,which has nine parameters and six freedom. We use the element to improve the existing result of the multigrid method of Morley element. The transfer operator of the new elment was defined and its properties was proved. Using these properties,we prove the convergence of the multigrid method of the new element for 4nd order elliptic problem.At last. We establish the program of multigrid method and do some numerical expriments.