带有阻尼项的非线性抛物积分微分方程的非协调混合有限元方法  

Nonconforming Mixed Finite Element Method for Nonlinear Integro-differential Equations of Parabolic Type with Damping

作　　者：李先枝 王建平[2] 陈丽 LI Xian-zhi;WANG Jian-ping;CHEN Li(School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, China;College of Information and Computational Science, Henan Agricultural University, Zhengzhou 450046, China)

机构地区：[1]郑州师范学院数学与统计学院,河南郑州450044 [2]河南农业大学信息与管理科学学院,河南郑州450046

出　　处：《数学的实践与认识》2018年第7期252-260,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271340,11671369);河南省高等学校重点科研项目(18B110021)

摘　　要：研究带有阻尼项的非线性抛物积分微分方程的非协调混合有限元（EQ1^rot＋Q10×Q01）方法，直接利用单元插值的性质，运用高精度分析和导数转移技巧，导出了半离散格式的超逼近性质，同时利用插值后处理技术，导出了相应的D（h^2）阶整体超收敛结果，并通过构造一个合适的外推格式得到了O（h^3）阶的外推解．In this paper, nonconforming mixed finite element method（EQ1^rot＋ Q10 × Q01） is studied for nonlinear integro-differential equations of parabolic type with damping. By utilizing the properties of the interpolation on the element ,high accuracy analysis and derivative delivery techniques, the corresponding superclose nature is obtained for semi-discrete scheme. At the same time, the O（h^2） order global superconvergence result is obtained by use of a postprocessing technique, and the extrapolation solution with order O（h^3） is devived by a suitable extrapolation scheme.

关 键 词：带有阻尼项的非线性抛物积分微分方程 非协调混合元格式 超逼近和超 收敛 外推 

分 类 号：O241.82[理学—计算数学]