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.

中文翻译：

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简化摩擦问题的虚拟单元法后验误差估计

我们研究了虚拟元素方法（VEM）的后验误差分析，以简化摩擦问题，这是第二种代表性椭圆变分不等式。通过将悬挂节点视为多边形元素的顶点，虚拟元素方法在自适应网格细化之后不需要任何局部网格后处理。在这项工作中，为设计自适应VEM以解决简化的摩擦问题，推导了残差型误差估计器。此外，证明了误差估计器的可靠性和效率。最后，通过数值例子验证了理论结果。