摘要
对一类非线性黏弹性方程利用双线性元Q_(11)及Q_(01)×Q_(10)元提出了一个低阶协调混合元格式.基于上述两个单元的高精度分析,利用平均值以及对时间变量的导数转移技巧,得到了原始变量u的H^1-模和中间变量p→=-(a(u)▽u+b(u)▽u_t)的L2-模意义下O(h^2)阶的超逼近性质.进一步借助插值后处理技术,导出了上述两个变量相应的超收敛结果.最后,通过构造一个合适的外推格式,得到O(h^3)阶的外推解.
With the help of the bilinear element Q_（11） and the Q_（01）× Q_（10） element,a low order conforming mixed finite element approximation scheme was proposed for nonlinear viscoelasticity type equations.Based on the high accuracy analysis of the two elements,mean-value approach and derivative delivery technique with respect to the time variable,the superclose properties with order O（ h^2） for the primitive solution in H^1-norm and the intermediate variable p→=-（ a（ u）▽u ＋ b（ u） ▽u_t） in L^2-norm were obtained,respectively. Furthermore,the corresponding superconvergence results about the two mentioned variable were presented through interpolated postprocessing approach,respectively. Finally,through constructing a suitable extrapolation scheme,the extrapolation solutions with order O（ h^3） were derived.
出处
《郑州大学学报（理学版）》
CAS
北大核心
2015年第4期12-16,共5页
Journal of Zhengzhou University:Natural Science Edition
基金
国家自然科学基金资助项目
编号11271340
关键词
非线性黏弹性方程
混合元方法
超收敛
外推
nonlinear viscoelasticity type equations
mixed finite element method
superconvergence
extrapolation
