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.
作者
杨怀君
YANG Huaijun(School of Mathematics,Zhengzhou University of Aeronautics,Zhengzhou 450046,China)
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)。
作者简介
杨怀君,男,河南长垣人,博士,副教授,研究方向为有限元方法。
