High Accuracy Eigenvalue Approximation by the Finite Element Method

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 3, 2011 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhimin Zhang – Wayne State University – http://www.math.wayne.edu/~zzhang/
Organizer
Yingjie Liu
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.