双调和特征值问题非协调有限元的多重校正方法

In this paper, we present a multi-level correction scheme for the biharmonic eigenvalue problem using the nonconforming finite element method. With the proposed method, the eigenvalue problem is transformed into an eigenvalue problem on the coarsest grid and a series of source problems on the fine grids. The multilevel correction scheme for the biharmonic eigenvalue problem possesses the high convergence rate and optimal computational cost provided that the linear solver for the nonconforming finite element method is optimal. Both theoretical analysis and numerical verification are presented.