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

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.