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高波数问题的超收敛性

本站小编 Free考研考试/2021-12-27

杜宇
湘潭大学数学与计算科学学院, 湘潭 411105
收稿日期:2017-08-26出版日期:2018-06-15发布日期:2018-05-15


基金资助:国家自然科学基金青年科学基金(11601026).


SUPERCONVERGENCE ANALYSIS FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBER

Du Yu
Department of Mathematics, Xiangtan University, Xiangtan 411105, China
Received:2017-08-26Online:2018-06-15Published:2018-05-15







摘要



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本文考虑求解Helmholtz方程的有限元方法的超逼近性质以及基于PPR后处理方法的超收敛性质.我们首先给出了矩形网格上的p-次元在收敛条件kkh2p+1C0下的有限元解和基于Lobatto点的有限元插值之间的超逼近以及重构的有限元梯度和精确解之间的超收敛分析.然后我们给出了四边形网格上的线性有限元方法的分析.这些估计都给出了与波数k和网格尺寸h的依赖关系.同时我们回顾了三角形网格上的线性有限元的超收敛结果.最后我们给出了数值实验并且结合Richardson外推进一步减少了误差.
MR(2010)主题分类:
65N12
65N15
65N30
78A40

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