### High Accuracy Eigenvalue Approximation by the Finite Element Method

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, October 3, 2011 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Zhimin Zhang – 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.