[1]刘 凯,黄学海,王文庆.四阶椭圆奇异扰动问题混合有限元方法[J].温州大学学报(自然科学版),2020,(02):024-30.
 LIU Kai,HUANG Xuehai,WANG Wenqing.Mixed Finite Element Method for Fourth-order Elliptic Singular Perturbation Problems[J].Journal of Wenzhou University,2020,(02):024-30.
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四阶椭圆奇异扰动问题混合有限元方法
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《温州大学学报》(自然科学版)[ISSN:1674-3563/CN:33-1344/N]

卷:
期数:
2020年02期
页码:
024-30
栏目:
数学
出版日期:
2020-05-25

文章信息/Info

Title:
Mixed Finite Element Method for Fourth-order Elliptic Singular Perturbation Problems
作者:
刘 凯1黄学海1王文庆2
1.温州大学数理与电子信息工程学院,浙江温州 325035; 2.温州商学院,浙江温州 325035
Author(s):
LIU Kai1 HUANG Xuehai1 WANG Wenqing2
1. College of Mathematics, Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, China 325035; 2. Wenzhou Business College, Wenzhou, China 325035
关键词:
四阶椭圆奇异扰动问题混合有限元方法混合变分问题误差估计
Keywords:
Fourth-order Elliptic Singular Perturbation Problems Mixed Finite Element Method Mixed Variation Problem Error Estimate
分类号:
O175.4
文献标志码:
A
摘要:
本文研究了四阶椭圆奇异扰动问题的Hellan-Herrmann-Johnson(HHJ)混合有限元方法.通过建立连续情形inf-sup条件,证明了四阶椭圆奇异扰动问题混合变分形式的适定性.进而定义网格依赖范数,建立离散情形的inf-sup条件,得到四阶椭圆奇异扰动问题HHJ混合有限元方法的适定性.最后,对HHJ混合有限元方法进行了误差分析.
Abstract:
In this paper, Hellan-Herrmann-Johnson (HHJ) mixed finite element method for fourth-order elliptic singular perturbation problems is studied. By establishing inf-sup conditions for continuous cases, the appropriateness of mixed variational formulas for fourth-order elliptic singular perturbation problems is proved. Then, the grid-dependent norm is defined, the inf-sup conditions for discrete cases are established, and the well-posedness of the HHJ mixed finite element method for the fourth-order elliptic singular perturbation problems is obtained. Finally, the error analysis of the HHJ mixed finite element method is carried out.

参考文献/References:

[1] Chen H, Chen S. Uniformly convergent nonconforming element for 3-D fourth order elliptic singular perturbation problem [J]. Comput Math, 2014, 32: 687-695.
[2] Chen H, Chen S, Qiao Z. C0-nonconforming tetrahedral and cuboid elements for the three dimensional fourth order elliptic problem [J]. Numer Math, 2013, 124: 99-119.
[3] Falk R S, Osborn J E. Error estimates for mixed methods [J]. RAIRO Anal Numer, 1980, 14(3): 249-277.
[4] Babuska I. The finite element method with Lagrangian multipliers [J]. Numer Math,1973, 20: 170-192.
[5] Brezzi F. On the existence uniqueness and approximation of saddle point problems arising from lagrange multipliers [J]. RAIRO Anal Numer, 1974, 8: 129-151.
[6] Nilssen T K, Tai X C, Winther R. A robust nonconforming H2-element [J]. Math Comp, 2000, 234(70): 489-505.
[7] Wang W Q, Huang X H, Tang K, et al. Morley-Wang-Xu element methods with penalty for a fourth order elliptic singular perturbation problem [J]. Adv Comput Math, 2018, 44(4): 1041-1061.
[8] Zulehner W. Nonstandard norms and robust estimates for saddle point problems [J]. Matrix Anal Appl, 2011, 2(32), 536-560.
[9] Babuska I, Osborn J, Pitkaranta J. Analysis of mixed methods using mesh dependent norms [J]. Math Comp, 1980, 35(152): 1039-1062.
[10] Comodi M I. The Hellan-Herrmann-Johnson method: some new error estimates and postprocessing [J]. Math Comp, 1989, 185(52): 17-29.

备注/Memo

备注/Memo:
收稿日期:2018-11-08
基金项目:国家自然科学基金项目(11771338)
作者简介:刘凯(1993- ),男,山西吕梁人,硕士研究生,研究方向:微分方程与动力系统
更新日期/Last Update: 2020-05-25