用有限元方法求解界面特征值问题

Finite Element Methods for Solving Interface Eigenvalue Problems

用有限元方法计算椭圆型界面特征值问题,实验数据显示近似特征值的变化规律:界面特征值问题中系数的间断性对协调和非协调Crouzeix-Raviart有限元特征值的收敛性并无影响,而且对协调有限元特征值外推以后得到高精度的解,相应的外推值还提供特征值下界;Crouzeix-Raviart元特征值提供特征值下界,这对一般有界区域如"镂空"型区域也成立.另外,还展示近似特征函数的图形.

In this paper, we solve interface eigenvalue problems by conforming and non- conforming finite element methods. The experiment data show that the optimal convergence rates may not be influenced by these discontinuous coefficients in interface eigenvalue problems and may be improved after extrapolation. The extrapolation eigenvalues and nonconforming Crouzeix-Raviart eigenvalues provide lower bounds of exact eigenvalues, which also holds for general bounded domains like hollow domains. Furthermore, the approximate eigenfunctions are displayed visually by use of figures.