In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose $C^1$ conforming virtual element method (VEM) of arbitrary order, $k\ge2$, to approximate the model problem numerically. We employ VEM to discretize the space variable and fully implicit scheme for temporal variable. Well-posedness of the fully discrete scheme is proved under certain conditions on the physical parameters, and we derive optimal order of convergence in both space and time variable. Finally, numerical experiments are presented to illustrate the behaviour of the proposed numerical scheme.

翻译：在本条中,我们考虑了非线性非局部时间依赖第四顺序方程式,表明一个细窄的矩形板的变形。我们提议1美元,即1美元,符合任意顺序的虚拟元件法(VEM),以数字方式估计模型问题。我们使用VEM将空间变量分离,并完全隐含时间变量方案。在物理参数的某些条件下,完全独立的方案被证明是完全独立的,我们在空间和时间变量中都得出最佳的趋同顺序。最后,我们用数字实验来说明拟议的数字方案的行为。