Applications Of A Second Order Nonconforming Finite Element

This paper mainly studies a second order nouconforming finite element method for both the second order elliptic problems and the evolution equation on the plane. In the third chapter, we constructs a new second order rectangular nonconforming finite element with 5NP degrees of freedom, which is used for convergence analysis of a general second order elliptic problem. Under the meaning of energy mode, interpolation error and consistency error of this finite element can achieve second order accuracy at the same time. However, some famous nonconformming element, such as classic Wilson clement, quasi-Wilson element, five-node element and rotated Q1 element can not do so.In the fourth chapter, the above finite element is used for the evolution equation. With-out using Ritz projection or the difference between the exact solution and interpolation of the problem is perpendicular to the finite element space, error estimates of the semi-discretization scheme and full-discretization scheme above the second order parabolic equation are obtained by means of the novel techniques. High order rectangular nonconforming finite element have rarely seen in the past literatures. So the research of this paper is very significant.