摘要
主要研究非线性抛物型积分微分方程的协调Galerkin有限元方法Crank-Nicolson(CN)全离散格式。通过对非线性项的精细估计,采用插值与投影相结合的估计技巧,导出了L^(∞)(H^(1))模意义下具有O(h^(2)+τ^(2))阶的超逼近性质。进一步利用插值后处理技术得到了整体超收敛结果,弥补了以往文献的不足。同时,通过数值例子验证了理论分析的正确性和方法的高效性。
The Crank-Nicolson(CN)fully discrete scheme of conforming Galerkin finite element method was mainly studied for the nonlinear parabolic integro-differential equation.By estimating the nonlinear term rigorously and using combination trick of the interpolation and projection,the supercloseness of order O(h^(2)+τ^(2))in L^(∞)(H^(1))norm was derived.Further,the global superconvergence result was obtained through interpolated post-processing technique,which covers the shortage in the previous literature.At the same time,a numerical example was provided to verify the correctness of the theoretical analysis and the high efficient of the proposed method.
作者
石东洋
张林根
SHI Dongyang;ZHANG Lingen(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)
出处
《信阳师范学院学报（自然科学版）》
CAS
2024年第1期45-50,共6页
Journal of Xinyang Normal University(Natural Science Edition)
基金
国家自然科学基金项目(12071443)。
