定常非线性薛定谔方程的有限元方法超收敛估计  

Superconvergence Estimation of Finite Element Method for the Time-Independent Nonlinear Schr9dinger Equation

作　　者：王建云 田智鲲[2] 

机构地区：[1]湖南工业大学理学院,湖南株洲412007 [2]湖南工程学院理学院,湖南湘潭411104

出　　处：《湘潭大学自然科学学报》2018年第1期24-26,共3页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金项目(11501485)

摘　　要：考虑了二维定常非线性薛定谔方程的超收敛问题.采用双线性矩形元将方程进行离散,利用椭圆投影算子得到了有限元解与精确解的投影在H1范数下的超收敛误差估计,并利用插值后处理技术获得了整体超收敛.This paper is concerned with the problem of superconvergence for a two-dimensional time-independent nonlinear Schrdinger equation.The equation is discretized by the bilinear rectangular element.The superconvergence error estimate between finite element solution and the elliptic projection of exact solution in H^1-norm is obtained by use of the elliptic projection operator.In addition,the global superconvergence is derived by use of the interpolation post-processing technique.

关 键 词：超收敛 薛定谔方程 有限元 插值后处理 

分 类 号：O241.82[理学—计算数学]