A nonconforming virtual element method for the Stokes problem on general meshes

摘要

In this paper, a nonconforming virtual element method for the Stokes problem is proposed and investigated. This method gives a unified scheme for two and three dimensions simultaneously. In addition, it provides an attractive computational feature treatment of general elements including non-convex and degenerate elements. Moreover, by choosing a proper low order velocity and pressure pair, we prove the discrete inf-sup condition for this method to obtain its solvability and stability. Furthermore, we show optimal energy norm error estimates for velocity and L-2 norm error estimates for both velocity and pressure. Finally, a series of numerical experiments are performed to validate that this method has good stability and accuracy for the Stokes problem. (C) 2017 Elsevier B.V. All rights reserved.