Improved defect-correction algorithms for the Navier–Stokes equations at small viscosity

In this article, based on finite element discretization, we propose some improved defect-correction algorithms for solving the stationary Navier–Stokes equations with small viscosity. The proposed algorithms are mainly inspired by the idea of the grad-div stabilized method and error correction technique. Maintaining the benefit of the usual defect-correction method, the proposed algorithms further improve the ability to solve problems with small viscosity and have a fast convergence rate. Moreover, stability analysis and error estimation of these algorithms are provided under the uniqueness requirement. Finally, some numerical experiments are tested to illustrate the effectiveness of the presented algorithms for small viscosity problem.