Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations

A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at t n + β tn+β with β ≥ 1 β ≥ 1 being a free parameter. It is shown that by choosing β = 3 , 6 , 9 β = 3, \,6,\,9 respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. These results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual backward differentiation formula (BDF) (i.e. β = 1 β =1 ) are not unconditionally stable while the new third- and fourth-order schemes with suitable β β are unconditionally stable and lead to expected convergence rates.