Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems

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

“…One way for this situation is to loose the stiffness of the finite element spaces. Mixed element method is then frequently used, and several schemes for the biharmonic eigenvalue problem with polynomials of low degree have been designed [1,19]. Also, some discretization schemes of mixed type for boundary value problems can be naturally utilized for the eigenvalue problem; we refer readers to [6] for related discussion.…”

Two-sided bounds of eigenvalues of second-and fourth-order elliptic operators

“…Indeed, the optimal order of convergence of the eigenvalues is O( u − u h 2 m,Ω ), where u is the corresponding exact eigenfunction. Obviously u − u h 2 0,Ω has higher order of accuracy and, moreover, it is easy to obtain the same high order of convergence for w − w h 2 m,Ω (see [2], [3], [29], [36]). Now, we will present the final step of our idea described as nonconformingconforming approach to eigenvalues approximation.…”

An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem

“…Particularly, Racheva and Andreev [24] have proposed a postprocessing method for the 2 -order self-adjoint eigenvalue problems by two-grid method or the two-space method. A similar method has been given for the Stokes eigenvalue problem [7,25], elliptic eigenvalue problem [16], and the biharmonic eigenvalue problem [26] by mixed finite element methods.…”