非线性Sobolev方程的一个协调扩展混合元新模式  

A New Conforming Expanded Mixed Finite Element Scheme for Nonlinear Sobolev Equation

作　　者：石东洋 郭龙飞 SHI Dongyang;GUO Longfei(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学数学与统计学院,河南郑州450001

出　　处：《信阳师范学院学报（自然科学版）》2023年第1期1-9,共9页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671369,12071443)。

摘　　要：基于双线性元Q11和零阶Nédélec元Q_(01)×Q_(10)所构成的单元对,对非线性Sobolev方程构造了一个协调扩展混合元新模式。根据单元的高精度特性,借助于插值和投影相结合方法、平均值技巧和插值后处理技术,导出了在半离散和二阶全离散格式下相关变量的超逼近和超收敛结果。同时,给出了一个数值例子,以验证理论分析的正确性。A new conforming expanded mixed finite element scheme is developed for nonlinear Sobolev equation with element pair of the bilinear element Q11and zero order Nédélec element Q_(01)×Q_(10).By use of the high accuracy characteristics of this element pair,and through the approach of combination of interpolation and projection,mean-value trick and the interpolated post-processing technique,the supercloseness and superconvergence results of relevant variables are derived for the semi-discrete and second order fully-discrete schemes.At the same time,a numerical example is provided to confirm the correctness of the theoretical analysis.

关 键 词：扩展混合有限元 非线性Sobolev方程 半离散及二阶全离散格式 超逼近和超收敛估计 

分 类 号：O241.82[理学—计算数学]