Euler implicit/explicit iterative scheme for the stationary Navier–Stokes equations

Abstract

In this paper, a new uniqueness assumption (A2) of the solution for the stationary Navier---Stokes equations is presented. Under assumption (A2), the exponential stability of the solution $$(\bar{u},\bar{p})$$ for the stationary Navier---Stokes equations is proven. Moreover, the Euler implicit/explicit scheme based on the mixed finite element is applied to solve the stationary Navier---Stokes equations. Finally, the almost unconditionally stability is proven and the optimal error estimates uniform in time are provided for the scheme.