河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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半线性粘弹性方程非常规Hermite型矩形元的高精度分析

河南城建学院数理学院, 河南平顶山 467044
DOI： 10.13763/j.cnki.jhebnu.nse.2016.01.004

High Accuracy Analysis of Unconventional Hermite-type Finite Element for Semi-linear Viscoelasticity Equations

MU Jingjing, ZHOU Shuke

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摘要/Abstract

摘要：

利用非常规的Hermite元对一类半线性粘弹性方程进行了有限元分析.首先给出了半离散格式下解的存在唯一性证明,同时利用插值和投影相结合的方法,借助于该元已有的高精度结果、平均值技巧和插值后处理技术,得到了H¹模意义下的超逼近和超收敛性质.最后给出了一种该方程的全离散逼近格式,在不需要网格比的情况下,得到了O(h³+τ²)的结果.

Abstract：

This paper studies a new unconventional Hermite-type FEMs for the semi-linear viscoelasticity equations.Firstly,it proves the existence and uniqueness of solution under the semi-discrete schemes.Based on the known high accuracy analysis,mean-value and postprocessing techniques,the superclose properties and the global superconvergence result in H¹-norm that are deduced by means of interpolation and projection technology combination.Finally,a fully-discrete schemes are constructed,and a lomplexity O(h³+τ²) is obtained without the meshes ratio in these schemes.

关键词

关键词： 半线性粘弹性方程 ; 非常规Hermite型有限元 ; 半离散和全离散 ; 超逼近和超收敛

Key words： semilinear viscoelasticity equations ; Hermite-type finite element ; semi-discrete and fully-discrete ; superclose and superconvergence schemes

参考文献 16

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