A residual-type a posteriori error estimation is developed for an interior penalty virtual element method (IPVEM) to solve a Kirchhoff plate bending problem. The computable error estimator is incorporated. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results on various benchmark tests confirm the robustness of the proposed error estimator and show the efficiency of the resulting adaptive VEM. (This is the initial version; additional content will be included in the final version.)

翻译：针对求解Kirchhoff板弯曲问题的内罚虚拟元方法（IPVEM），本文发展了一种残差型后验误差估计方法。该方法包含了可计算的误差估计子。通过构造一个加益算子并建立若干相关误差估计，我们推导了后验误差界的可靠性与有效性。作为该误差估计子的应用，我们基于单悬挂节点规则的网格细化策略，引入了一种自适应虚拟元方法。多个基准测试的数值结果证实了所提误差估计子的鲁棒性，并展示了所得自适应虚拟元方法的有效性。（此为初始版本；最终版本将包含更多内容。）