Curved Boundaries Nonconforming Finite Element Method

In this paper two nonconforming elements' approximations to second order elliptic boundary value problem and stationary Stokes equations in the domain with curved boundaries are considered, respectively. By use of the novel approaches and techniques and the peculiarities of elements, the difficulties which rise from the changed domain and the boundary datum and disposal of curved boundary and the nonconforming characters of elements are overcome. The optimal error estimates are obtained. Thus the applications of nonconforming finite elements are extended.