High Accuracy Eigenvalue Approximation by the Finite Element Method

Applied and Computational Mathematics Seminar
Monday, October 3, 2011 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Wayne State University
Finite element approximations for the eigenvalue problem of the Laplace  operator are discussed. A gradient recovery scheme is proposed to enhance  the finite element solutions of the eigenvalues. By reconstructing the  numerical solution and its gradient, it is possible to produce more accurate  numerical eigenvalues. Furthermore, the recovered gradient can be used to  form an a posteriori error estimator to guide an adaptive mesh refinement.  Therefore, this method works not only for structured meshes, but also for  unstructured and adaptive meshes. Additional computational cost for this  post-processing technique is only O(N) (N is the total degrees of freedom),   comparing with O(N^2) cost for the original problem.