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计算数学  2015 

非线性Schr?dinger方程新混合元方法的高精度分析

, PP. 162-178

Keywords: 非线性Schr?,dinger方程,双线性元,新混合元方法,超逼近和超收敛,半离散和全离散格式

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Abstract:

基于双线性元及其梯度所属空间,建立了非线性Schr?dinger方程的自由度少且易满足B-B条件的新混合元格式.首先,利用双线性元的高精度分析和导数转移技巧,在半离散格式下,导出了原始变量在H1模及流量在L2模意义下的超逼近性质,进而,借助于插值后处理算子,得到了整体超收敛结果.最后,对向后Euler和Crank-Nicolson-Galerkin全离散格式分别给出了原始变量的H1模及c模和流量的L2模误差分析,并通过数值算例,表明逼近格式是高效的.

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