Isaac Scientific Publishing

# Journal of Advances in Applied Mathematics

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

Download PDF (584.1 KB) PP. 139 - 145 Pub. Date: October 6, 2020

### Author(s)

• Zhiyun Yu*
College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
• Dongyang Shi
Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
• Huiqing Zhu
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^1-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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