Abstract
We propose a simple nonconforming virtual element for plate bending problems, which has few local degrees of freedom and provides the optimal convergence in \(H^2\)-norm. Moreover, we prove the optimal error estimates in \(H^1\)- and \(L^2\)-norm. The nonconforming virtual element is constructed for any order of accuracy, but not \(C^0\)-continuous. It is worth mentioning that, for the lowest-order case on triangular meshes the simplified nonconforming virtual element coincides with the well-known Morley element, so it can be taken as the extension of the Morley element to polygonal meshes. Finally, we verify the optimal convergence in \(H^2\)-norm for the nonconforming virtual element by some numerical tests.
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Acknowledgements
We would like to thank Jiming Wu, Zhiming Gao and Shuai Su from Institute of Applied Physics and Computational Mathematics, Beijing, China, for the provision of the polygonal mesh data and specially for the encouragement to carry on with this work. We also thank Donatella Marini and Claudia Chinosi from Italy, for the guidance to compute the errors of VEM.
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This work is supported by National Natural Science Foundation of China (11701522, 11371331), National Key Research and Development Program of China (2016YFB0201304) and National Magnetic Confinement Fusion Science Program of China (2015GB110003).
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Zhao, J., Zhang, B., Chen, S. et al. The Morley-Type Virtual Element for Plate Bending Problems. J Sci Comput 76, 610–629 (2018). https://doi.org/10.1007/s10915-017-0632-3
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DOI: https://doi.org/10.1007/s10915-017-0632-3