An abstract framework of the virtual element method is established for solving general elliptic hemivariational inequalities with or without constraint, and a unified a priori error analysis is given for both cases. Then, virtual element methods of arbitrary order are applied to solve three elliptic hemivariational inequalities arising in contact mechanics, and optimal order error estimates are shown with the linear virtual element solutions. Numerical simulation results are reported in several contact problems; in particular, the numerical convergence orders of the lowest order virtual element solutions are shown to be in good agreement with the theoretical predictions.

中文翻译：

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广义椭圆半变分不等式的虚元法

建立了求解有或无约束的广义椭圆半变分不等式的虚拟元素方法的抽象框架，并针对这两种情况给出了统一的先验误差分析。然后，应用任意阶虚拟元素方法来解决在接触力学中产生的三个椭圆半变不等式，并用线性虚拟元素解决方案给出了最佳阶误差估计。数值模拟结果报告了几个接触问题。特别是，最低阶虚拟单元解的数值收敛阶数表明与理论预测吻合良好。