对流扩散方程的分裂混合有限体积元方法  

Splitting Mixed Finite Volume Element Method for Convection Diffusion Equations

作　　者：王慧芳 李宏 方志朝[1] 赵洁[1,2] WANG Hui-fang;LI Hong;FANG Zhi-chao;ZHAO Jie(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;College of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古财经大学统计与数学学院,呼和浩特010070

出　　处：《内蒙古大学学报（自然科学版）》2018年第3期253-261,共9页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11761053;11701299);内蒙古自治区自然科学基金(2016BS0105;2017MS0107);内蒙古自治区高等学校青年科技英才支持计划(NJYT-17-A07);内蒙古自治区"草原英才"

摘　　要：将分裂思想和混合有限体积元方法相结合,在三角网格剖分下数值求解一类二维对流扩散方程.通过使用最低阶Raviart-Thomas混合有限元空间,并引入迁移算子把试探函数空间映射成检验函数空间,构造了半离散和全离散的分裂混合有限体积元格式.利用迁移算子的性质得到了离散格式的最优阶误差估计.最后给出数值实验结果验证了理论分析结果以及该方法的有效性.By combination of the splitting with the mixed finite volume element method,a numerical solution of a class of two-dimensional convection diffusion equation is given based on triangular grids.Semi-discrete and fully-discrete splitting mixed finite volume element schemes are constructed by using the lowest order Raviart-Thomas mixed finite element space and introducing a transfer operator that maps the trial function space into the test function space.Optimal error estimates for discrete schemes are obtained by using the properties of transfer operators.Finally,numerical experiments are given to verify the theoretical results and the effectiveness of the proposed schemes.

关 键 词：对流扩散方程 分裂混合有限体积元方法 最优阶误差估计 

分 类 号：O241.82[理学—计算数学]