A Multi-level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation
arXiv:1606.05419
Abstract
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization. Then, we construct multi-level finite element schemes by implementing the algorithm as in [33] to the nested discretizations on series of nested grids. The multi-level mixed scheme for biharmonic eigenvalue problem possesses optimal convergence rate and optimal computational cost. Both theoretical analysis and numerical verifications are presented.