特征值问题的Lagrange型各向异性有限元方法

Lagrange Type Conforming Finite Element Methods for Eigenvalue Problems on Anisotropic Meshes

在各向异性网格下首先研究了二阶椭圆特征值问题算子谱逼近的若干抽象结果.然后将这些结果具体应用于线性和双线性Lagrange型协调有限元,得到了与传统有限元网格剖分下相同的最优误差估计,从而拓宽了已有的成果.

Some abstract conclusions for the spectrum approximation of compact operators to the second order elliptic eigenvalue problems are first studied on the anisotropic meshes. These results then are applied to Lagrange type linear and bilinear finite elements respectively. The optimal error estimates are obtained which are the same as on the conventional regular or quasi-uniform meshes. Thus the results of traditional finite element methods are extended.