对流扩散反应方程的一个稳定化混合有限元

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.

A stabilized mixed finite element method for convection-diffusion-reaction equations

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.