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Conforming Rectangular Mixed Finite Elements for Elasticity

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Abstract

We present a new family of rectangular mixed finite elements for the stress-displacement system of the plane elasticity problem. Based on the theory of mixed finite element methods, we prove that they are stable and obtain error estimates for both the stress field and the displacement field. Using the finite element spaces in this family, an exact sequence is established as a discrete version of the elasticity complex in two dimensions. And the relationship between this discrete version and the original one is shown in a commuting diagram.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450001, China

    Shao-Chun Chen

  2. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ya-Na Wang

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  1. Shao-Chun Chen
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  2. Ya-Na Wang
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Correspondence to Ya-Na Wang.

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Chen, SC., Wang, YN. Conforming Rectangular Mixed Finite Elements for Elasticity. J Sci Comput 47, 93–108 (2011). https://doi.org/10.1007/s10915-010-9422-x

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  • DOI: https://doi.org/10.1007/s10915-010-9422-x

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