Schrodinger方程双线性元的超收敛分析和外推  

Superconvergence analysis and extrapolation of bilinear finite element for Schrodinger equation

作　　者：王萍莉[1] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]郑州大学数学与统计学院,河南郑州450001

出　　处：《山东大学学报（理学版）》2014年第10期66-71,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11101381,11271340)

摘　　要：研究了Schrdinger方程双线性有限元逼近。利用导数转移技巧和该单元的高精度结果,得到了H1模意义下O(h2)阶的超逼近性质。同时利用插值后处理技术,给出了H1模意义下整体超收敛结果。近一步地,通过构造一个新的外推格式,导出了比传统有限元误差高两阶的O(h3)阶的外推解。The bilinear finite element approximation is mainly discussed for Schrdinger equation. The superclose property with O （h^2） order is obtained in H^1-norm by use of the derivative transfering skill and the high accuracy results of the element. Also,the global superconvergence result is given in H^1-norm through the interpolation post-processing technique. Furthermore,through constructing a new extrapolation scheme,the extrapolation solution with O（h^3） order is deduced which is two order higher than the traditional error estimate.

关 键 词：SCHRODINGER方程 双线性元 超收敛 外推 

分 类 号：O212.6[理学—概率论与数理统计]