多项时间分数阶扩散方程的二次三角形元超收敛分析  

Superconvergence analysis of quadratic triangular element for multi-term time-fractional diffusion equations

作　　者：牛裕琪[1] 王萍莉[1] 王芬玲[1] Niu Yuqi;Wang Pingli;Wang Fenling(School of Mathematics and Statistics,Xuchang University,Xuchang 461000,China)

机构地区：[1]许昌学院数学与统计学院,河南许昌461000

出　　处：《河南师范大学学报（自然科学版）》2020年第2期20-26,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11101381,11971416);河南省高等学校重点科研项目(19B110013);许昌市基础与前沿研究项目(19,154001).

摘　　要：基于二次三角形有限元和时间L1逼近格式,建立了具有Caputo导数的多项时间分数阶扩散方程的全离散格式.首先,在均匀网格下利用积分恒等式技巧证明了关于二次三角形元的高精度结果.其次运用分数阶导数的处理技巧和插值与投影之间的关系导出了空间方向的超逼近结果和时间方向的最优误差估计.进一步,借助插值后处理技术,得到了超收敛估计.Based on the quadratic triangular finite element and time L1 approximate scheme,a fully-discrete scheme is established for multi-term time-fractional diffusion equation with Caputo derivative.Firstly,the high accuracy precision result of the quadratic triangular element is proved by using the integral identity technique under the uniform grid.Then,the spatial superclose result and temporal optimal error estimate are obtained by using the fractional derivative technique and the relationship between interpolation and projection. Furthermore,the superconvergence analysis is given through the interpolated postprocessing technique.

关 键 词：多项时间分数阶扩散方程 二次三角形元 全离散格式 超逼近和超收敛 

分 类 号：O242.21[理学—计算数学]