| Abstract: | In this article, we develop a branch of nonsingular solutions of a Picard multilevel stabilization of mixed finite volume method for the 2D/3D stationary Navier‐Stokes equations without relying on the unique solution condition. The method presented consists of capturing almost all information of initial problem (the nonlinear problems) on the coarsest mesh and then performs one Picard defect correction (the linear problems) on each subsequent mesh based on previous information thus only solving one large linear systems. What is more, the method presented can results in a better coefficient matrix in the model presented with small viscosity. Theoretical results show that the method presented is derived with the convergence rate of the same order as the corresponding finite volume method/finite element method solving the stationary Navier‐Stokes equations on a fine mesh. Therefore, the method presented is definitely more efficient than the standard finite volume method/finite element method. Finally, numerical experiments clearly show the efficiency of the method presented for solving the stationary Navier‐Stokes equations.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 34: 30–50, 2018 |
