Bounds for Eigenvalues with the Use of Finite Elements
Bounds for Eigenvalues with the Use of Finite Elements
复制标题
使用有限元确定特征值的界限
DOI：
10.1007/978-3-7091-6282-8_6
复制
发表时间：
2001
影响因子：
2.3
通讯作者：
U. Mertins
中科院分区：
文献类型：
--
作者：
H. Behnke;U. Mertins
计算了自伴偏微分方程特征值问题的最小特征值的验证上界和下界。上界由Rayleigh-Ritz方法获得，合适的Goerisch方法提供下界。试函数的构造与有限元的使用。所有的计算都是用区间算术进行的，因此结果不会受到舍入误差的影响。数值结果给出了L形膜。
Verified upper and lower bounds for the smallest eigenvalues of eigenvalue problems with self-adjoint partial differential equations are computed. Upper bounds are obtained by the Rayleigh-Ritz method, a suitable Goerisch method provides lower bounds. The trial functions are constructed with the use of finite elements. All computations are carried out with intervaI arithmetic thus the results are protected against rounding errors. Numerical results are given for the L-shaped membrane.