The nonconforming virtual element method for fourth-order singular perturbation problem

被引：0
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作者：
Bei Zhang
Jikun Zhao
Shaochun Chen
机构：
[1] Henan University of Technology,College of Science
[2] Zhengzhou University,School of Mathematics and Statistics
来源：
Advances in Computational Mathematics | 2020年 / 46卷
关键词：
Nonconforming virtual element; Fourth-order singular perturbation problem; Polygonal mesh; 65N30; 65N12;
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摘要：
We present the nonconforming virtual element method for the fourth-order singular perturbation problem. The virtual element proposed in this paper is a variant of the C0-continuous nonconforming virtual element presented in our previous work and allows to compute two different projection operators that are used for the construction of the discrete scheme. We show the optimal convergence in the energy norm for the nonconforming virtual element method. Further, the lowest order nonconforming method is proved to be uniformly convergent with respect to the perturbation parameter. Finally, we verify the convergence for the nonconforming virtual element method by some numerical tests.
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