汇报标题 (Title)：A modified interior penalty virtual element method for fourth-order singular perturbation problems（针对四阶奇怪摄动问题的建改内罚虚构元步骤）
汇报人 (Speaker)：余跃 副教授 （湘潭大学）
汇报功夫 (Time)：2025年4月19日 (周六) 10:30
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：纪丽洁
主办部门：理学院数学系
提要：This work is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM). Compared with the original IPVEM proposed by Zhao et al., the study introduces modifications to the jumps and averages in the penalty term, as well as presents a mesh-dependent selection of the penalty parameter. Drawing inspiration from the modified Morley finite element methods, we leverage the conforming interpolation technique to handle the lower part of the bilinear form in the error analysis. We establish the optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case.
