Conforming and Nonconforming Virtual Element Methods for a Kirchhoff Plate Contact Problem
Conforming and Nonconforming Virtual Element Methods for a Kirchhoff Plate Contact Problem
复制标题
基尔霍夫板接触问题的相容和非相容虚拟元素方法
DOI：
10.1093/imanum/draa005
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发表时间：
2020
影响因子：
2.1
通讯作者：
Jikun Zhao
中科院分区：
文献类型：
--
作者：
Fei Wang;Jikun Zhao
本文建立了一个通用的框架来研究协调虚元法和非协调虚元法求解带摩擦的Kirchhoff板接触问题，这是一个第二类四阶椭圆变分不等式.由于摩擦接触，该VI包含不可微项。该理论框架适用于现有的虚元，如协调元、C^0 $-连续元和全连续Morley型元。在统一的框架中，我们推导出这些虚拟元素的先验误差估计，并表明它们实现了最低阶情况下的最佳收敛阶。为了证明VEM的性能，我们提出了一些数值结果，证实了理论预测的收敛阶。
We establish a general framework to study the conforming and nonconforming virtual element methods (VEMs) for solving a Kirchhoff plate contact problem with friction, which is a fourth-order elliptic variational inequality (VI) of the second kind. This VI contains a non-differentiable term due to the frictional contact. This theoretical framework applies to the existing virtual elements such as the conforming element, the $C^0$-continuous nonconforming element and the fully nonconforming Morley-type element. In the unified framework we derive a priori error estimates for these virtual elements and show that they achieve optimal convergence order for the lowest-order case. For demonstrating the performance of the VEMs we present some numerical results that confirm the theoretical prediction of the convergence order.