Isaac Scientific Publishing
Journal of Advances in Applied Mathematics
JAAM > Volume 5, Number 4, October 2020

Least-Squares Method of EQ1rot Nonconforming Finite Element for Convection-Diffusion Problems

DOI: 10.22606/jaam.2020.54001

Author(s)
Zhiyun Yu, Dongyang Shi, Huiqing Zhu
Affiliation(s)
College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
Mathematics Department, University of Southern Mississippi, Hattiesburg MS, 39406, U.S.A
Abstract
In this paper, a least-squares method of EQ_1^rot nonconforming finite element(NFE) is proposed for convection-diffusion problems. The existence and uniqueness of the approximate solutions are proved. The convergence analysis is presented and the optimal order error estimates for the stress under H(div)-norm and the displacement under broken H<sup>1</sup>-norm are derived. At last, some numerical results are presented to verify the theoretical analysis, which show that our method is stable and performs very well.
Keywords
convection-diffusion problems, EQ_1^rot NFE, least-squares method, optimal order error estimates
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