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Journal of Scientific Computing

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28-12-2017

The Morley-Type Virtual Element for Plate Bending Problems

Authors: Jikun Zhao, Bei Zhang, Shaochun Chen, Shipeng Mao

Published in: Journal of Scientific Computing | Issue 1/2018

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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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Title: The Morley-Type Virtual Element for Plate Bending Problems
Authors: Jikun Zhao
Bei Zhang
Shaochun Chen
Shipeng Mao
Publication date: 28-12-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0632-3

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