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

• DOI: 10.1016/j.cma.2017.03.027
• Publication Date: 2017-04-05T17:01:29Z
• Authors: Xin Liu; Jian Li; Zhangxin Chen
• Keywords: Stokes problem

Abstract 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.