CIP-stabilized virtual elements for diffusion-convection-reaction problems

The Virtual Element Method (VEM) for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence of polynomial projection operators, typical of the VEM, the stability and the error analysis requires particular care-especially in treating the advective term. Some numerical tests are presented to support the theoretical results.