Investigations on two kinds of two-grid mixed finite element methods for the elliptic eigenvalue problem

Two kinds of two-grid new mixed finite element schemes for the elliptic eigenvalue problem based on less regularity of flux are considered. In the new mixed variational formulation, the flux belongs to the square integrable space instead of the classical H(div), and the choices of finite element pairs become simple and easy. The two-grid methods consist of solving a small elliptic eigenvalue problem on the coarse mesh and then solving a linear algebraic system on the fine mesh, which can still maintain asymptotically optimal accuracy. Finally, the performance of two kinds of two grid schemes are compared in efficiency and precision aspects by a series of numerical experiments. Numerical results show that the accelerated two-grid method is a viable choice for the lowest order approximations of the elliptic eigenvalue problem.