拟线性抛物问题各向异性R-T混合元分析

J4 ›› 2012, Vol. 47 ›› Issue (2): 36-41.

拟线性抛物问题各向异性R-T混合元分析

孟晓然¹,石东伟²

1.许昌学院数学与统计学院, 河南许昌 461000; 2.河南科技学院数学系, 河南新乡 453003

收稿日期:2011-01-29 出版日期:2012-02-20 发布日期:2012-12-24
作者简介:孟晓然(1982- ),女,硕士,讲师,研究方向为有限元方法. Email: xcxxmxr@163.com
基金资助:
国家自然科学基金数学天元基金资助项目(11026154);河南省教育厅自然科学基金资助项目(2010A110018)

Analysis of the anisotropic R-T element for quasi-linear parabolic problems on anisotropic meshes

MENG Xiao-ran¹, SHI Dong-wei²

1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, Henan, China

Received:2011-01-29 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

利用各向异性判别定理证明了一阶R-T混合元的各向异性特征,并把它应用于拟线性抛物方程,在不需要Ritz投影的前提下, 直接利用插值算子给出了相关变量的收敛性分析和误差估计,利用积分恒等式技巧,导出了流量在H(div,Ω)模意义下的超逼近性质。

关键词: 拟线性抛物方程;R-T元;各向异性;超逼近

Abstract:

The anisotropic property of the R-T element with one order is proved based on the anisotropic interpolation theorem and applied to quasi-linear parabolic problems. The convergence analysis and error estimates are directly given through an interpolation operator without Ritz projection, and by use of integral identity, the supercloseness of flux is derived in H(div,Ω)-norm.

Key words: quasi-linear parabolic problems; R-T element; anisotropy; supercloseness

孟晓然1,石东伟2. 拟线性抛物问题各向异性R-T混合元分析[J]. J4, 2012, 47(2): 36-41.

MENG Xiao-ran1, SHI Dong-wei2. Analysis of the anisotropic R-T element for quasi-linear parabolic problems on anisotropic meshes[J]. J4, 2012, 47(2): 36-41.

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