A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem
A Posteriori Error Estimates of Virtual Element Method for a Simplified Friction Problem
复制标题
简化摩擦问题的虚拟元法后验误差估计
DOI：
10.1007/s10915-020-01242-9
复制
发表时间：
2020
影响因子：
2.5
通讯作者：
Huayi Wei
中科院分区：
文献类型：
--
作者：
Yanling Deng;Fei Wang;Huayi Wei
研究了一个简化摩擦问题的虚拟元法的后验误差分析，该摩擦问题是一个典型的第二类椭圆变分不等式。虚拟单元法将悬挂节点视为多边形单元的顶点，在网格自适应加密后不需要任何局部网格后处理。在这项工作中，残差型误差估计器的设计自适应VEM解决简化的摩擦问题。此外，还证明了误差估计的可靠性和有效性。最后给出了一个数值例子来验证理论结果。
We study a posteriori error analysis of the virtual element method (VEM) for a simplified friction problem, which is a representative elliptic variational inequality of the second kind. By treating hanging nodes as vertices of polygonal elements, the virtual element method does not require any local mesh post-processing after the adaptive mesh refinement. In this work, residual type error estimators are derived for designing adaptive VEM to solve the simplified friction problem. Furthermore, the reliability and efficiency of the error estimators are proved. Finally, a numerical example is given to verify the theoretical results.