We study a nonconforming virtual element method (VEM) for advection-diffusion-reaction problems with continuous interior penalty (CIP) stabilization. The design of the method is based on a standard variational formulation of the problem (no skew-symmetrization), and boundary conditions are imposed with a Nitsche technique. We use the enhanced version of VEM, with a ``DoFi-DoFi'' stabilization in the diffusion and reaction terms. We prove stability of the proposed method and derive $h$-version error estimates.
翻译:本文研究一种针对对流-扩散-反应问题的非协调虚拟元方法(VEM),该方法采用连续内罚(CIP)稳定化技术。该方法的设计基于问题的标准变分形式(无需斜对称化处理),并通过Nitsche技术施加边界条件。我们采用增强版VEM,在扩散项与反应项中引入“自由度-自由度”(DoFi-DoFi)稳定化机制。我们证明了所提方法的稳定性,并推导出$h$版本误差估计。