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STABILIZED NONCONFORMING MIXED FINITE ELEMENT METHOD FOR LINEAR ELASTICITY ON RECTANGULAR OR CUBIC MESHES

Bei Zhang1, Jikun Zhao2, Minghao Li1, Hongru Chen1   

  1. 1. School of Sciences, Henan University of Technology, Zhengzhou 450001, China;
    2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
  • Received:2020-06-01 Revised:2021-01-27 Online:2022-11-15 Published:2022-11-18
  • Contact: Jikun Zhao, Email: jkzhao@zzu.edu.cn
  • Supported by:
    This work is partially supported by National Natural Science Foundation of China (No. 12001170), Key Scientific Research Projects in Colleges and Universities in Henan Province (No. 21A110009) and Research Foundation for Advanced Talents of Henan University of Technology (No. 2018BS013).

Bei Zhang, Jikun Zhao, Minghao Li, Hongru Chen. STABILIZED NONCONFORMING MIXED FINITE ELEMENT METHOD FOR LINEAR ELASTICITY ON RECTANGULAR OR CUBIC MESHES[J]. Journal of Computational Mathematics, 2022, 40(6): 865-881.

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the L2-norm for stress and in the broken H1-norm and L2-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.

CLC Number: 

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