This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in the penalty term, as well as presents an automated 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. Through our analysis, we establish optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case.

翻译：本文致力于利用文献[42]提出的内罚虚元方法(IPVEM)求解四阶奇异摄动问题。研究对罚项中的跳跃量与平均值进行了修正，并提出了基于网格自适应选择的罚参数选取策略。受修正Morley有限元方法的启发，我们利用协调插值技术处理双线性型中的低阶部分。通过分析，我们在能量范数下建立了最优收敛性，并针对最低阶情形给出了关于摄动参数一致收敛的严格证明。