A new nonconforming mixed finite element scheme for second order eigenvalue problem

A new nonconforming mixed finite element method (MFEM for short) is established for the Laplace eigenvalue problem. Firstly, the optimal order error estimates for both the eigenvalue and eigenpair (the original variable u and the auxiliary variable (p) over right arrow - del u) are deduced, the lower bound of eigenvalue is estimated simultaneously. Then, by use of the special property of the nonconforming EQ(1)(rot) element (the consistency error is of order 0(h(2)) in broken H-1 -norm, which is one order higher than its interpolation error), the techniques of integral identity and interpolation postprocessing, we derive the superclose and superconvergence results of order 0(h(2)) for u in broken H-1 -norm and (p) over right arrow in L-2-norm. Furthermore, with the help of asymptotic expansions, the extrapolation solution of order 0(h(3)) for eigenvalue is obtained. Finally, some numerical results are presented to validate our theoretical analysis. (C) 2015 Elsevier Inc. All rights reserved.