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A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems

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Abstract

A new conforming discontinuous Galerkin method is studied for the linear elasticity interface problems with discontinuous coefficients and displacement. This new method is based on a new definition of weak gradient operator and has no stabilizer. The weak divergence operator used in the scheme is different from the weak Galerkin finite element method, which significantly reduces the computational cost. The error estimates of optimal order in discrete \(L^2\) and \(H^1\) norms are established. Numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method, and to illustrate the locking-free property.

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Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions, which lead to a significant improvement of this manuscript. The authors’ work was partially supported by National Natural Science Foundation of China under Grant Nos. 11871038, 11771367 and 12131014.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Yue Wang & Fuzheng Gao

  2. Department of Mathematics, Jinan University, Guangzhou, 510632, Guangdong, China

    Jintao Cui

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  1. Yue Wang
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  2. Fuzheng Gao
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Correspondence to Fuzheng Gao.

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Wang, Y., Gao, F. & Cui, J. A Conforming Discontinuous Galerkin Finite Element Method for Linear Elasticity Interface Problems. J Sci Comput 92, 9 (2022). https://doi.org/10.1007/s10915-022-01857-0

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  • DOI: https://doi.org/10.1007/s10915-022-01857-0

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