Two-grid nonconforming finite element method for second order elliptic problems

In this paper, we present and analyze two-grid P1 nonconforming finite element method for second order elliptic problems. The two-grid method involves solving one small origin problem on coarse grid with grid size H, and some correction problems on local fined grids with grid size h. If h = O(H2) is chosen, we show that the convergence rate of this two-grid method is optimal in broken H1-norm. Numerical results conforming the theory are also provided.