论文标题
非线性非局部动力板方程的虚拟元素方法的收敛分析
Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation
论文作者
论文摘要
在本文中，我们考虑了非线性非局部时间依赖性的第四阶方程，证明了狭窄且狭窄的矩形板的变形。我们提出了$ c^1 $符合任意顺序的虚拟元素方法（VEM），$ k \ ge2 $，以数字近似模型问题。我们使用VEM来离散空间变量，并为时间变量离散完全隐式的方案。在某些条件下，在物理参数的某些条件下证明了完全离散方案的适合性，我们得出了时空和时间变量的最佳收敛顺序。最后，提出了数值实验，以说明提出的数值方案的行为。
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.
