Pengzhan Huang, Xiaoling Ma and Tong Zhang: Superconvergence of a nonconforming finite element method for the stationary Navier-Stokes equations, p.159-174

Abstract:

Superconvergence results are established for a nonconforming finite element approximation of the stationary Navier-Stokes equations by a $L^2$-projection method. This nonconforming finite element method adopts the Crouzeix-Raviart element for the velocity and the continuous piecewise linear element for the pressure. The current paper complements the work of Li and Chen (2008) [6], which presents this pair of mixed finite element method for the Stokes equations. Numerical results are shown to support the developed theory analysis.

Key Words: Superconvergence, Navier-Stokes equations, $L^2$-projection, Nonconforming finite element, inf-sup condition.

2000 Mathematics Subject Classification: Primary: 35Q30;
Secondary: 65N30, 65N12.