摘要
本文针对对流扩散反应方程提出了一个稳定化混合有限元格式,该格式基于混合有限元法与最小二乘法的结合.在此格式中,由于最小二乘稳定项的引入,有限元逼近空间的选取无需满足经典的Ladyzhenkaya-Babuska-Brezzi(LBB)稳定性条件,从而对两个变量的有限元逼近可以方便地使用等阶有限元组合.对于定常的对流扩散反应方程,本文获得了有限元的稳定性,对误差进行了估计,并以数值算例验证了理论分析和格式的有效性.对于非定常的对流扩散反应方程,本文给出了有限元的误差估计和数值算例.
In this paper,we propose a stabilized finite element for the convection-diffusion-reaction equations.This finite element combines the mixed finite element with the least-squares method.Due to the introduced least-square stability term,the selection of finite element spaces does not need to satisfy the classical Ladyzhenkaya-Babuska-Brezzi(LBB)stability condition.As a result,the finite element approximation of the two variables can conveniently use equal order finite elements.For the steady convection-diffusion-reaction equations,we obtain the stability and give the error estimate for the finite element and exemplify the theoretical analysis and reliability by numerical experiments.For the unsteady convection-diffusion-reaction equations,we estimate the error and give an example for the finite element.
作者
杨星月
杨荣奎
冯民富
YANG Xing-Yue;YANG Rong-Kui;FENG Min-Fu(School of Mathematics,Sichuan University,Chengdu 610064,China)
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第5期37-44,共8页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(11971337)。
关键词
对流扩散反应方程
稳定化方法
混合有限元
LBB稳定性条件
Convection-diffusion-reaction equation
Stabilized method
Mixed finite element
LBB stability condition
