对流扩散方程的时间间断时空有限体积元法  

A time-discontinuous space-time finite volume element method for convection-diffusion equations

作　　者：肖宇宇 何斯日古楞 杨凯丽 XIAO Yu-yu;HE Si-riguleng;YANG Kai-li(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;Hohhot Minzu College,Hohhot,010051,China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021 [2]呼和浩特民族学院,内蒙古呼和浩特010051

出　　处：《高校应用数学学报（A辑）》2021年第2期179-192,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11501311,11761053);内蒙古自然科学基金(2018MS01020,2017MS0107);呼和浩特民族学院科研创新团队建设计划项目和校级项目。

摘　　要：将时间间断的时空元思想与基于等距节点下三次Lagrange插值的超收敛有限体积元方法相结合,以三次Lagrange插值导数超收敛点为对偶剖分节点,引入插值投影算子,建立对流扩散方程的时间间断时空有限体积元格式.结合有限体积元分析与以Radau积分点为节点的Lagrange插值,证明了近似解的最优L^(∞)(L^(2))-模误差估计.用单元正交分解法证明了格式在时间节点处的超收敛估计.最后给出数值算例验证了理论分析结果以及该方法的可行性和有效性.In this paper,the time-discontinuous space-time element idea is combined with the super-convergent finite volume element method based on cubic Lagrange interpolation under equidistant nodes,and the super-convergence point of cubic Lagrange interpolation derivative is taken as the dual split point,interpolation projection operator is introduced to establish the time-discontinuous space-time finite volume element format of the convection-diffusion equation.Combing the finite element analysis with Lagrange interpolation polynomials fixed by Radau integral points,in order to prove the approximate solution of the optiaml error estimates of L^(∞)(L^(2))norm.The superconvergent estimation of the scheme at the time node is proved by orthogonal decomposition method.Finally,a numerical example to confirm the theroetical analysis results as well as the feasibility and effectiveness of the method.

关 键 词：对流扩散方程 时间间断时空有限体积元 最优误差估计 

分 类 号：O241.82[理学—计算数学]