Abstract
In this paper, we propose a locking-free stabilized mixed finite element method for the linear elasticity problem, which employs a jump penalty term for the displacement approximation. The continuous piecewise k-order polynomial space is used for the stress and the discontinuous piecewise \((k-1)\)-order polynomial space for the displacement, where we require that \(k\ge 3\) in the two dimensions and \(k\ge 4\) in the three dimensions. The method is proved to be stable and k-order convergent for the stress in \(H(\mathrm {div})\)-norm and for the displacement in \(L^2\)-norm. Further, the convergence does not deteriorate in the nearly incompressible or incompressible case. Finally, the numerical results are presented to illustrate the optimal convergence of the stabilized mixed method.
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Acknowledgements
We would like to thank the anonymous referee. His suggestions help us to better show our results in the current version.
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This work is supported by National Natural Science Foundation of China (11371331, 11501524), Key scientific research projects in colleges and universities in Henan Province (18A110030), Startup Research Fund of Zhengzhou University (32210515).
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Zhang, B., Zhao, J., Chen, S. et al. A locking-free stabilized mixed finite element method for linear elasticity: the high order case. Calcolo 55, 12 (2018). https://doi.org/10.1007/s10092-018-0255-6
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DOI: https://doi.org/10.1007/s10092-018-0255-6