Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations

• DOI: 10.1137/050639910
• Publication Date: 2007-04-26T22:00:21Z
• Authors: Yinnian He; Weiwei Sun
• Keywords: Linear multistep method; Crank–Nicolson method

In this paper, we study the stability and convergence of Crank–Nicolson/Adams–Bashforth scheme for two‐dimensional nonstationary Navier–Stokes equations. A finite element method is applied spatial approximation velocity pressure. The time discretization based on Crank–Nicolson linear term explicit Adams–Bashforth nonlinear term. Moreover, present optimal error estimates prove that almost unconditionally stable convergent, i.e., convergent when step less than or equal to a constant.