非线性黏弹性方程双线性元解的高精度分析

J4 ›› 2011, Vol. 46 ›› Issue (8): 31-37.

非线性黏弹性方程双线性元解的高精度分析

牛裕琪^1,王芬玲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:2011-01-31 出版日期:2011-08-20 发布日期:2011-09-08
作者简介:牛裕琪(1969- ),女,副教授,主要从事有限元方法及应用研究. Email: niuyuqi003@126.com
基金资助:
国家自然科学基金数学天元基金(11026154);河南省教育厅自然科学基金资助项目(2010A110018;2011A110020)

Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations

NIU Yu-qi¹, WANG Fen-ling¹, SHI Dong-wei²

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

Received:2011-01-31 Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

利用积分恒等式和平均值技巧,给出了非线性黏弹性方程的双线性元逼近,得到了H¹模意义下的O(h²)阶超逼近性质。同时借助插值后处理技术,导出了整体超收敛结果。在此基础上, 通过构造合适的外推格式,得到了具有更高精度O(h³)阶的近似解。

关键词: 非线性黏弹性方程;双线性元;高精度分析;插值后处理;外推

Abstract:

In this paper, by use of the integral identities and the mean value technique, approximation of bilinear finite element for the nonlinear viscoelasticity type equations with superclose property of order O(h²) in H¹-norm is obtained. A global superconvergence result is yielded by interpolated post-processing method. Then higher accuracy of order O(h³) for approximation solution is derived through constructing a proper extrapolation scheme.

Key words: nonliear viscoelasticity type equations; bilinear element; higher accuracy; interpolated post-processing; extrapolation

牛裕琪1,王芬玲1,石东伟2. 非线性黏弹性方程双线性元解的高精度分析[J]. J4, 2011, 46(8): 31-37.

NIU Yu-qi1, WANG Fen-ling1, SHI Dong-wei2. Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations[J]. J4, 2011, 46(8): 31-37.

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