汇报标题 (Title)：A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates
（基尔霍夫板问题的内罚虚构元步骤的后验误差估计）
汇报人 (Speaker)：冯方 副钻研员（漯河理工大学）
汇报功夫 (Time)：2025年11月18日 (周二) 15:00
汇报地址 (Place)：腾讯会议 898-819-227
约请人(Inviter)：纪丽洁
主办部门：理学院数学系
提要：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.
