拟线性粘弹性方程新H^1-Galerkin最低阶混合元格式的高精度分析  

High Accuracy Analysis of a New H^1-Galerkin Lowest Order Mixed Finite Element Scheme for Quasi-linear Viscoelasticity Equations

作　　者：王芬玲[1] 樊明智[1] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]郑州大学数学与统计学院,河南许昌450001

出　　处：《应用数学》2017年第1期40-55,共16页Mathematica Applicata

基　　金：国家自然科学基金(11271340);河南省教育厅自然科学基金项目(14A110009;16A110022;17A110011);2016年许昌市科技局项目

摘　　要：利用双线性元和零阶Raviart-Thomas元,针对拟线性粘弹性方程建立新的H^1-Galerkin混合元逼近格式.在半离散格式下,给出原始变量u的H^1模和应力=?ut的H(div;?)模的超逼近性和超收敛结果.同时,导出向后欧拉格式和Crank-Nicolson-Galerkin格式的最优误差估计.最后,通过数值算例表明逼近格式是有效的.A lowest order H1-Galerkin mixed finite element approximation scheme is proposed for a class of quasi-linear viscoelasticity equations with the bilinear element and zero order Raviart-Thomas. The superclose properties and superconvergence results of the original variable u and stress p→ =△ut in Hi-norm and H（div; Ω）-norm are derived for semi-discrete scheme. At the same time, optimal error estimates are deduced for the Euler and Crank-Nicolson fully-discrete schemes. Finally, it is shown that the proposed approximate schemes are effective by numerical examples.

关 键 词：拟线性粘弹性方程 超逼近与超收敛 H^1-GALERKIN混合有限元方法 半离散和全离散格式 

分 类 号：O242.21[理学—计算数学]