非结构四边形网格下的一类保对称有限体元格式  

Symmetry-preserving Finite Volume Element Scheme on Unstructured Quadrilateral Grids

作　　者：聂存云[1] 舒适[1] 盛志强[2] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]北京应用物理与计算数学研究所,北京100088

出　　处：《计算物理》2009年第2期175-183,共9页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(10771178,10676031);国家863高技术惯性约束聚变专题;教育部重点(208093);湖南省教育厅重点(07A068);国家973(2005CB321702)资助项目

摘　　要：针对定常扩散问题,在非结构四边形网格下,通过选取特殊的控制体和有限体元空间,建立两种保对称有限体元格式,在拟一致网格剖分下,当扩散系数光滑时,证明有限体元解函数在L2和H1范数下均具有饱和误差阶.数值实验验证理论结果的正确性,同时表明新格式对扭曲大变形四边形网格、间断系数问题具有较强的适应性.在正交网格下,第二种格式对流(flux)函数在单元中心点的值还具有超逼近性.With special control volumes and finite volume element spaces, two symmetry-preserving finite volume element schemes for stationary diffusion problems are established on unstructured quadrilateral grids. Saturated order of error in L2-norm and Ht -norm for discrete solutions under quasi-uniform partition is demonstrated as diffusion coefficient is smooth. Numerical examples verify theoretical results. It shows strong adaptability of the scheme on distorted quadrilateral grids and for diffusion problems with non-smooth coefficient. The second scheme shows super-approximation for flux function at central point of element as grids are orthogonal.

关 键 词：非结构四边形网格 保对称有限体元格式 扩散方程 误差估计 

分 类 号：O241.82[理学—计算数学]