UC Irvine

We present stabilized virtual element methods for convection-diffusion problems in the convection-dominated regime. In the context of finite element methods, the edge-averaged finite element schemes were successfully applied to convection-dominated problems. We aim to generalize the edge-averaged stabilization to the virtual element framework. Hence, we develop the edge-averaged virtual element methods that produce numerical solutions on polygonal meshes without spurious oscillations caused by small diffusion coefficients. Well-posedness of the discrete problem and convergence analysis are provided. We also show numerical experiments which support theoretical results, and display numerical solutions with sharp boundary layers in the convection-dominated regime.