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.

中文翻译：

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四阶奇异摄动问题的非协调虚拟元方法

我们提出了针对四阶奇异摄动问题的非协调虚拟元方法。本文提出的虚拟元素是我们先前工作中介绍的C ^0-连续不合格虚拟元素的一种变体，它允许计算用于构造离散方案的两个不同的投影算子。我们为不合格虚拟元素方法显示了能量范数的最佳收敛。此外，最低阶不符合方法被证明相对于扰动参数是一致收敛的。最后，我们通过一些数值测试验证了非合格虚拟元素方法的收敛性。