A Weak Galerkin Finite Element Method Can Compute Both Upper and Lower Eigenvalue Bounds
A Weak Galerkin Finite Element Method Can Compute Both Upper and Lower Eigenvalue Bounds
复制标题
DOI：
10.1007/s10915-022-01986-6
复制
发表时间：
2022-09
影响因子：
2.5
通讯作者：
Qigang Liang;Xuejun Xu;Liuyao Yuan
中科院分区：
文献类型：
--
作者：
Qigang Liang;Xuejun Xu;Liuyao Yuan
本文对特征值问题的弱Galerkin（WG）逼近，观察到一个有趣的现象，即只有通过调整全局罚参数，才能从上到下得到精确特征值的良好逼近.在此基础上，设计了一种高精度的特征值计算算法，以获得更高的收敛阶数和更低的计算开销。发展了一些新的技术来分析特征值的上下界性质。数值结果支持我们的理论。
In this paper, we observe an interesting phenomenon for a weak Galerkin (WG) approximation of eigenvalue problems, that is, we may obtain good approximations for exact eigenvalues from below or above, only through adjusting the global penalty parameter. Based on this observation, a high accuracy algorithm for computing eigenvalues is designed to yield higher convergence order with lower expenses. Some new techniques are developed to analyze upper and lower bound properties of eigenvalues. Numerical results supporting our theory are given.