Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation
Numerical Analysis
2022-02-08 v1 Numerical Analysis
Analysis of PDEs
Abstract
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 conforming virtual element method (VEM) of arbitrary order, , 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.
Cite
@article{arxiv.2202.02368,
title = {Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation},
author = {D. Adak and D. Mora and S. Natarajan},
journal= {arXiv preprint arXiv:2202.02368},
year = {2022}
}