曲面上对流-扩散-反应方程的两种稳定化混合有限元方法的数值比较  

Numerical Comparison of Two Stabilized Mixed Finite Element Methods for Convection-Diffusion-Equations on Surfaces

作　　者：金孟晴 冯新龙[1] 何银年[1,2] JIN Mengqing;FENG Xinlong;HE Yinnian(School of Mathematics and Systems Sciences,Xinjiang University,Urumqi Xinjiang 830017,China;School of Mathematics and Statistics,Xi’an Jiaotong University,Xi’an Shaanxi 710049,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《新疆大学学报（自然科学版）（中英文）》2022年第3期266-274,282,共10页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：新疆维吾尔自治区重点实验室开放课题(2020D04002).

摘　　要：研究了曲面对流-扩散-反应方程的有限元逼近问题.通过引入不同形式的中间变量,分别将原方程转化为等价的一阶混合形式.运用混合有限元的思想,直接使用低阶有限元对(P_(1)-P_(1))近似的混合稳定化方法.该方法不仅满足inf-sup条件,而且对于对流占优情况所产生的非物理震荡,可以将其有效地捕捉.最后,数值实验结果表明,测试的收敛结果与已知理论一致.In this paper,the finite element approximation of the convection-diffusion-reaction equation on surfaces is studied.By introducing middle variables of different forms,the original equation is transformed into the equivalent,first-order mixed form.Using the idea of mixed finite element,this paper directly uses the mixed stabilization method of low order finite element pair(P_(1)-P_(1)) approximation.The method not only satisfies the well-posed condition,but also can effectively capture the non-physical oscillation caused by convective dominance.Finally,the numerical results show that the convergence results are consistent with the known theory.

关 键 词：曲面对流-扩散-反应方程 曲面混合有限元方法 稳定化方法 INF-SUP条件 

分 类 号：O242.21[理学—计算数学]