Streamline Diffusion Virtual Element Method for Convection-Dominated Diffusion Problems

Abstract

A novel streamline diffusion form of virtual element method for convection-dominated diffusion problems is studied. The main feature of the method is that the test function in the stabilised term has the adjoint operator-like form (−∇·($K$(x)∇$v$)−b(x)·∇$v$). Unlike the standard VEM, the stabilisation scheme can efficiently avoid nonphysical oscillations. The well-posedness of the problem is also proven and error estimates are provided. Numerical examples show the stability of the method for very large Péclet numbers and its applicability to boundary layer problem.