Schrdinger方程各向异性有限元超收敛分析

Superconvergence Analysis of Anisotropic Finite Element for Schrdinger Equation

讨论了在半离散格式下的各向异性双线性元对Schrdinger方程的逼近.首先利用该单元的特殊性质,在没有利用对网格正则性和拟一致假设的条件下得到了与传统方法相同的超逼近性质,然后基于插值后处理的技巧,构造出合适的插值算子,得到了整体超收敛的结果.

In this paper, bilinear finite element approximation to Sehrtidinger equation on anisotropic meshes under semidiserete scheme is discussed. Firstly, without the shape regularity assumption and inverse assumption on the meshes, the same superelose prop- erties as the traditional methods are derived through the special properties of the element. Furthermore, based on the interpolated post- processing technique, a suitable interpolation operator is constructed, then the global supereonvergenee is obtained.