A Multi-Level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation

In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits natural nested discretization. Then, we present multi-level finite element schemes by implementing the algorithm as in Lin and Xie (Math Comput 84:71–88, 2015) to the nested discretizations on a series of nested grids. The multi-level mixed scheme for the biharmonic eigenvalue problem possesses optimal convergence rate and optimal computational cost. Both theoretical analysis and numerical verifications are presented.