Variational multiscale virtual element method for the convection-dominated diffusion problem. (July 2021) - Xie, Cong; Wang, Gang; Feng, Xinlong
Abstract: In this paper a new stabilized virtual element method for the convection-dominated diffusion problem is proposed. By taking advantage of robustness of variational multiscale method and flexibility of virtual element method, the proposed method is proven to be very easy to implement. The adding stabilized term in the variational formulation can be calculated directly using the stability portion of the virtual element method. There is no user-defined parameter. And the priori error estimate can be easily obtained as there is no change in the consistency portion in the virtual element method. Numerical experiments show good agreement with the theoretical convergence rate and validate the stabilization effect.