• 论文 •

### 对流扩散反应方程的局部投影稳定化连续时空有限元方法

1. 1. 内蒙古大学数学科学学院, 呼和浩特 010021;
2. 包头师范学院数学科学学院, 包头 014030
• 收稿日期:2019-11-06 出版日期:2021-08-15 发布日期:2021-08-20
• 通讯作者: 李宏,E-mail:malhong@imu.edu.cn.
• 基金资助:
由国家自然科学基金（11761053），内蒙古自然科学基金（2021MS01018，2019BS01010），内蒙古自治区草原英才，内蒙古自治区青年科技英才-领军人才项目（NJYT-17-A07）资助.

Dong Ziming, Li Hong, Zhao Zhihui, Tang Siqin. LOCAL PROJECTION STABILIZATION CONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION-REACTION EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(3): 367-387.

### LOCAL PROJECTION STABILIZATION CONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION-REACTION EQUATIONS

Dong Ziming1,2, Li Hong1, Zhao Zhihui1, Tang Siqin1

1. 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China;
2. Faculty of Mathematics, Baotou Teachers'College, Baotou 014030, China
• Received:2019-11-06 Online:2021-08-15 Published:2021-08-20

In this paper, local projection stabilization method and continuous space-time finite element method are combined to study convection-diffusion-reaction equations. The discrete form of stabilized continuous space-time Galerkin method is constructed. The ideas discussed here are different from the traditional space-time finite element method. The approaches presented here have the advantages of reducing calculation and simplifying theoretical analysis with the techniques of Lagrange interpolation polynomials in time direction, which not only can decouple time and space variables but also reduce the dimensions of the spacetime finite element solution. The stability analysis of finite element solution is obtained by Legendre polynomials. Moreover, the error estimates in global L(L2)-norm and local L2(Jn; LPS)-norm are proved with Lobatto polynomials. Finally, numerical examples are given to verify correctness of the theoretical analysis and feasibility and validity of the stabilization scheme.

MR(2010)主题分类:

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