學術活動
数学科学学院学术报告：High Accuracy eigenvalue approximation by the finite element method
2008-12-30
來源：科技處 點擊次數：單位： 数学科学学院
學術活動名称：學術報告
學術活動主题：High Accuracy eigenvalue approximation by the finite element method
主持（講）人 ：Zhimin Zhang 教授（Department of Mathematics, Wayne State University）
時間： 2008年12月30日（星期二）下昼4：00-5：00
地點： 数学科学学院412课堂
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.
