Two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping

Abstract

By combining the defect-correction method with the two-level discretization strategy and the local pressure projection stabilized method, this paper presents and studies two kinds of two-level defect-correction stabilized algorithms for the simulation of 2D/3D steady Navier-Stokes equations with damping, where the lowest equal-order P1−P1 finite elements are used for the velocity and pressure approximations. In the proposed algorithms, an artificial viscosity stabilized nonlinear Navier-Stokes problem with damping is first solved in the coarse grid defect step, and then corrections are computed in the fine grid correction step by solving a linear problem based on Oseen-type and Newton-type iterations, respectively. Under the uniqueness condition, stability of the proposed algorithms is analyzed, and optimal error estimates of the approximate solutions are deduced. The correctness of the theoretical predictions and the effectiveness of the proposed algorithms are illustrated by some 2D and 3D numerical results.