A new two-level defect-correction method for the steady Navier–Stokes equations

Abstract

A new defect-correction method based on subgrid stabilization for the simulation of steady incompressible Navier–Stokes equations with high Reynolds numbers is proposed and studied. This method uses a two-grid finite element discretization strategy and consists of three steps: in the first step, a small nonlinear coarse mesh system is solved, and then, in the following two steps, two Newton-linearized fine mesh problems which have the same stiffness matrices with only different right-hand sides are solved. The nonlinear coarse mesh system incorporates an artificial viscosity term into the Navier–Stokes system as a stabilizing factor, making the nonlinear system easier to resolve. While the linear fine mesh problems are stabilized by a subgrid model defined by an elliptic projection into lower-order finite element spaces for the velocity. Error bounds of the approximate solutions are estimated. Algorithmic parameter scalings are derived from the analysis. Effectiveness of the proposed method is also illustrated by some numerical results.