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ACCURACY ANALYSIS OF 12-PARAMETER RECTANGULAR PLATE ELEMENTS WITH GEOMETRIC SYMMETRY

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Systems Science and Mathematical Sciences 2000年第2期13卷 146-151页

作者： shi dongyang CHEN Shaochun (Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China) 郑州大学数学系河南郑州 450052 郑州大学数学系河南郑州

In this paper, it is proved that the double set parameter rectangular plate elements with geometric symmetry possess a very special convergence property, i.e., the consistency error due to nonconformity is of order O(h2) which is one order higher than that of ACM element and rectangular generalized conforming element proposed by Y. Q. Long, although all these elements have the same asympotical rate of convergence O(h) in the energy norm. This particular property seems to be never seen before for other nonconforming rectangular plate elements.

关键词： Nonconforming rectangular element geometric symmetry special convergence.

A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2007年第4期16卷 289-299页

作者： dongyang shi Lifang Pei Shaochun Chen Department of Mathematics Zhengzhou University Zhengzhou 450052 China Department of Mathematics and Physics Luoyang Institute of Science and Technology Luoyang 471003 China

The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral *** error estimates are derived,which are the same as tho... 详细信息

关键词：误差估计麦克斯韦方程式任意四边形非一致性元素

Superconvergence of a Nonconforming Finite Element Approximation to Viscoelasticity Type Equations on Anisotropic Meshes

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2006年第4期15卷 375-384页

作者： dongyang shi Yucheng Peng Shaochun Chen Department of Mathematics Zhengzhou University Zhengzhou 450052 China

The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover, employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied.

关键词：黏弹性型函数 Crouzeix-Raviart型元素后加工各向异性网目

Facile synthesis of vesicle-like nanoscale zerovalent iron with high dispersion and high removal performance towards nitrobenzene reduction

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Facile synthesis of vesicle-like nanoscale zerovalent iron w...

AN ANISOTROPIC NONCONFORMING FINITE ELEMENT METHOD FOR APPROXIMATING A CLASS OF NONLINEAR SOBOLEV EQUATIONS

河南省化学会2016年学术年会

作者： dongyang shi Xia Zhang Jing Fan School of Environment Henan Key Laboratory for Environmental Pollution Control Key Laboratory for Yellow River and Huai River Water Environment and Pollution Control Ministry of Education Henan Normal University Henan Institute of Technology

Nanoscale zerovalent iron(NZVI), with large specific surface area, high reaction activity and strong reductive power, is increasingly being used for the degradation of environmental contaminants. Rapid aggregation and deactivation hinder the wide application of NZVI. In this paper, the novel NZVI was successfully prepared by templated self-assembly of block copolymers without inert gas protection. Various characterization techniques(XRD, FTIR, SEM-EDX, TEM, DLS) were used to figure out the synthesis pathways. More interestingly, the novel vesicle-like NZVI showed some surprising features such as uniform nanometer sizes, unique morphologies and high dispersion. We selected Cr(VI) as a model to verify the stability of vesicle-like NZVI. Compared with bare nanoscale zerovalent(BNZVI), it is satisfactory that the removal of Cr(VI) only decreased from 100% to 95.6% in the vesicle-like NZVI treatment over 90 days, whilst the removal of Cr(VI) by BNZVI dramatically decreased from 60.1% to 12.0% under the same reaction conditions. Furthermore, the synthesized vesicle-like NZVI was used to catalyze nitrobenzene(NB)degradation in simulated wastewater. We found that NB degradation capacities of the vesicle-like NZVI could be enhanced by being encapsulated in vesicles, where a large improvement(approx. 2.95 and 2.48 times higher for k and qe, respectively compared with BNZVI) was observed, and the reduction of NB fitted the pseudo-second order equation better. The novel NZVI dramatically showed a very good chemical stability,while still maintained its high reactivity. Such excellent performance might be attributed to the presence of block copolymer micelles(vesicles), which can hinder well the strong agglomeration of metal particles and prevent metal particles from being oxidized.

关键词： vesicle-like nanoscale zerovalent iron self-assembly block copolymers nitrobenzene

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Journal of Computational Mathematics 2009年第Z1期 299-314页

作者： dongyang shi Haihong Wang Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China Yuepeng Du Department of Computer,Nanyang Institute of Technology,Nanyang 473004,China

An anisotropic nonconforming finite element method is presented for a class of nonlinearSobolev *** optimal error estimates and supercloseness are obtained for bothsemi-discrete and fully-discrete approximate schemes,which are the same as the traditionalfinite element *** addition,the global superconvergence is derived through thepostprocessing *** experiments are included to illustrate the feasibilityof the proposed method.

关键词： Nonlinear Sobolev equations Anisotropic Nonconforming finite element Supercloseness Global superconvergence

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非对称不定问题双线性元的超收敛和外推

应用数学 2013年第1期26卷 220-227页

作者：史艳华石东洋许昌学院数学与统计学院河南许昌461000 郑州大学数学系河南郑州450052

本文主要讨论非对称不定问题的双线性有限元逼近.在不需要引入Ritz投影的前提下直接利用单元上的插值并借助于该元已有的高精度分析和平均值技巧,得到在H1模意义下O(h2)阶的超逼近和整体超收敛结果.同时给出两个新的误差渐近展开式,导... 详细信息

本文主要讨论非对称不定问题的双线性有限元逼近.在不需要引入Ritz投影的前提下直接利用单元上的插值并借助于该元已有的高精度分析和平均值技巧,得到在H1模意义下O(h2)阶的超逼近和整体超收敛结果.同时给出两个新的误差渐近展开式,导出比传统有限元误差高两阶的O(h3)阶的外推解.

关键词：非对称不定问题双线性元高精度分析超收敛及其外推

半线性伪双曲方程最低阶的H^1-Galerkin混合元方法

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系统科学与数学 2015年第5期35卷 514-526页

作者：石东洋史艳华郑州大学数学与统计学院郑州450052 许昌学院数学与统计学院许昌461000

研究在半离散和全离散格式下,半线性伪双曲方程最低阶的协调H^1-Galerkin混合有限元逼近.具体地,用双线性元逼近原始变量u,用零阶Raviart-Thomas(R-T)元逼近流量p.首先通过泰勒展式和积分恒等式技巧得到了p的一个新的误差估计式.然后,... 详细信息

研究在半离散和全离散格式下,半线性伪双曲方程最低阶的协调H^1-Galerkin混合有限元逼近.具体地,用双线性元逼近原始变量u,用零阶Raviart-Thomas(R-T)元逼近流量p.首先通过泰勒展式和积分恒等式技巧得到了p的一个新的误差估计式.然后,导出了u在H^1模和p在H(div;Ω)模意义下的超逼近性质,改进了已有文献的结果.

关键词：半线性伪双曲方程 H1-Galerkin混合元方法最低阶协调有限元半离散和全离散格式超逼近性质

各向异性网格上抛物方程全离散格式的高精度分析

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数学物理学报（A辑） 2009年第4期29卷 898-911页

作者：石东洋龚伟郑州大学数学系郑州450052

该文的主要目的是在各向异性网格下,利用双二次有限元逼近对抛物方程全离散格式进行了高精度分析,通过积分恒等式技巧以及一些新的技术得到了超逼近结果.

关键词：高精度分析抛物方程双二次元各向异性网格

双曲积分微分方程类Wilson非协调元的超收敛和外推

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系统科学与数学 2012年第7期32卷 880-892页

作者：史艳华石东洋许昌学院数学与统计学院许昌461000 郑州大学数学系郑州450052

将类Wilson非协调元方法应用于半离散格式下双曲积分微分方程的逼近.当问题的精确解u∈H^3(Ω)/H^4(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h^2)/O(h^3)阶(比其插值误差高一阶/两阶)的特殊性质,并结合双线性元的高精度分析... 详细信息

将类Wilson非协调元方法应用于半离散格式下双曲积分微分方程的逼近.当问题的精确解u∈H^3(Ω)/H^4(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h^2)/O(h^3)阶(比其插值误差高一阶/两阶)的特殊性质,并结合双线性元的高精度分析和插值后处理技巧,得到了与以往文献中双线性元完全相同的O(h^2)阶的超逼近性质和整体超收敛结果.进而,通过构造一个新的外推格式导出了具有三阶精度的外推解.

关键词：双曲积分微分方程类Wilson非协调元高精度分析超收敛及其外推.