抛物积分微分方程的Crank-Nicolson全离散格式下的超收敛分析  

Superconvergent Error Anylysis of Crank-Nicolson Fully Discrete Schemes for Parabolic Integral-differential Equation

作　　者：杨怀君 孟金涛[1] 周永卫[1] YANG Huaijun;MENG Jintao;ZHOU Yongwei(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《郑州航空工业管理学院学报》2023年第1期101-108,共8页Journal of Zhengzhou University of Aeronautics

基　　金：国家自然科学基金(12101568)。

摘　　要：文章基于低阶协调的双线性元在矩形网格下的高精度积分恒等式,在时间方向使用具有二阶精度的Crank-Nicolson离散格式,再利用插值与投影相结合的技巧,给出了抛物积分微分方程的全离散格式下的超逼近和超收敛的误差估计。最后,通过数值试验验证了理论分析的正确性。This paper is based on the high-precision integral identity of low-order conforming bilinear element on rectangular meshes,and the Crank Nicolson discrete scheme with second-order accuracy in time direction,combining the Ritz projection operator and the interpolation operator,and providing the superapproximation and superconvergence error analysis under the fully discrete scheme for parabolic-integro differential equations.Finally,the correctness of the theoretical analysis is verified by numerical experiments.

关 键 词：抛物积分微分方程 双线性元 Crank-Nicolson全离散格式 超逼近和超收敛误差估计 

分 类 号：O242.21[理学—计算数学]