Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of thin and narrow rectangular plate. We propose $$C^1$$ conforming virtual element method (VEM) arbitrary order, $$k\ge 2$$ , to approximate model problem numerically. employ VEM discretize space variable fully implicit scheme for temporal variable. Well-posedness discrete is proved under certain conditions on physical parameters, derive optimal convergence in both Finally, numerical experiments are presented illustrate behaviour proposed scheme.