报告题目 (Title)：A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates
中文题目：基尔霍夫板问题的内罚虚拟元方法的后验误差估计
报告人 (Speaker)：冯方 副研究员 南京理工大学
报告时间 (Time)：2025年11月18日 (周二) 15:00
报告地点 (Place)：腾讯会议 898-819-227
邀请人(Inviter)：纪丽洁
报告摘要：In this talk, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in Feng and Yu (2024), we adopt a modified discrete variational formulation that incorporates the H1-elliptic projector in the jump and average terms. This allows us to simplify the numerical implementation by including the H1-elliptic projector in the computable error estimators. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with C0-continuous interior penalty finite element methods. As observed in the a priori analysis, the interior penalty virtual elements exhibit similar behaviors to C0-continuous elements despite its H1-nonconforming. This observation extends to the a posteriori estimate since we do not need to account for the jumps of the function itself in the discrete scheme and the error estimators. 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 from several benchmark tests confirm the robustness of the proposed error estimators and show the efficiency of the resulting adaptive VEM.