单位： 数学科学学院

学术活动名称：学术报告

学术活动主题：High Accuracy eigenvalue approximation by the finite element method

主持（讲）人 ：Zhimin Zhang 教授（Department of Mathematics, Wayne State University）

时间：  2008年12月30日（星期二）下午4：00-5：00

地点： 数学科学学院412教室

备注：

Abstract: Finite element approximation for the eigenvalue problem of the Laplace operator is discussed. Two recovery schemes are 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.  In addition, the methodology can be applied to more general eigenvalue problems.