A new streamline diffusion finite element method for the generalized Oseen problem

doi:10.1007/s10483-018-2296-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (2): 291-304.doi: https://doi.org/10.1007/s10483-018-2296-6

• 论文 • 上一篇

A new streamline diffusion finite element method for the generalized Oseen problem

Chao XU¹, Dongyang SHI², Xin LIAO²

1. Faculty of Mathematics and Physics Education, Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

收稿日期:2017-05-02 修回日期:2017-07-25 出版日期:2018-02-01 发布日期:2018-02-01
通讯作者: Dongyang SHI E-mail:shi_dy@zzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11271340 and 11671369)

A new streamline diffusion finite element method for the generalized Oseen problem

Chao XU¹, Dongyang SHI², Xin LIAO²

1. Faculty of Mathematics and Physics Education, Luoyang Institute of Science and Technology, Luoyang 471023, Henan Province, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received:2017-05-02 Revised:2017-07-25 Online:2018-02-01 Published:2018-02-01
Contact: Dongyang SHI E-mail:shi_dy@zzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11271340 and 11671369)

摘要/Abstract

摘要： This paper aims to present a new streamline diffusion method with low order rectangular Bernardi-Raugel elements to solve the generalized Oseen equations. With the help of the Bramble-Hilbert lemma, the optimal errors of the velocity and pressure are estimated, which are independent of the considered parameter ε. With an interpolation postprocessing approach, the superconvergent error of the pressure is obtained. Finally, a numerical experiment is carried out to confirm the theoretical results.

关键词: KKM theorem, matching theorem, fixed point, minimax inequality, streamline diffusion method, Oseen problem, superconvergent error estimate, Bernardi-Raugel element

Abstract: This paper aims to present a new streamline diffusion method with low order rectangular Bernardi-Raugel elements to solve the generalized Oseen equations. With the help of the Bramble-Hilbert lemma, the optimal errors of the velocity and pressure are estimated, which are independent of the considered parameter ε. With an interpolation postprocessing approach, the superconvergent error of the pressure is obtained. Finally, a numerical experiment is carried out to confirm the theoretical results.

Key words: KKM theorem, matching theorem, fixed point, minimax inequality, streamline diffusion method, superconvergent error estimate, Oseen problem, Bernardi-Raugel element

中图分类号:

65N30
65N15

Chao XU, Dongyang SHI, Xin LIAO. A new streamline diffusion finite element method for the generalized Oseen problem[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(2): 291-304.

参考文献

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A new streamline diffusion finite element method for the generalized Oseen problem

A new streamline diffusion finite element method for the generalized Oseen problem

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