Kirchhoff型抛物方程的Galerkin有限元法的超收敛误差分析  

Superconvergence Error Analysis of Galerkin Finite Element Method for Kirchhoff-type Parabolic Equations

作　　者：杨怀君 YANG Huaijun(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5期108-112,共5页Journal of Zhengzhou University of Aeronautics

基　　金：国家自然科学基金项目(12101568)。

摘　　要：文章研究了后向Euler全离散Galerkin格式下的Kirchhoff型抛物方程的超收敛误差分析。首先,讨论了数值解的先验误差估计,并证明了数值解的存在唯一性。其次,使用双线性元的高精度误差估计以及Ritz投影算子与插值算子相结合的技术,通过技巧性地处理非线性项得到了超逼近的误差估计结果。再次,通过插值后处理方法获得了整体的超收敛结果。最后,通过数值试验验证了理论分析的正确性。In this paper,the superconvergence error analysis is investigated for a Kirchhoff type parabolic equation with backward Euler fully discrete Galerkin scheme.Firstly,a priori error estimate for the numerical solution is discussed and the existence and the uniqueness of the numerical solution are proved.Subsequently,in terms of the high accuracy error estimate of the bilinear element and the technique of combining the Ritz projection operator with the interpolation operator,the superclose error estimate is derived by skillfully dealing with the nonlinear term.Then,the global superconvergence result is obtained by a interpolation postprocessing approach.Finally,a numerical experiment is carried out to verify the correctness of the theoretical findings.

关 键 词：Kirchhoff型抛物方程 后向Euler全离散Galerkin格式 超逼近和超收敛误差估计 

分 类 号：O242.21[理学—计算数学]