A two-grid characteristic finite element method for incompressible flow

Abstract

This study proposes and briefly analyzes a two-grid characteristic finite element method based on a residual technique, with the low order pair of mixed finite element such as $P_1-P_1$, for the incompressible time-dependent Navier–Stokes equations. A characteristic finite element calculation of nonlinear Navier–Stokes problem is first presented on a coarse grid, followed by the residual correction on a fine grid utilizing the difference between the coarse and fine grids. The characteristic method is transported by divergence-free velocity field, free of the Newton iterations, unconditionally stable, and free of stabilization for large Reynolds numbers of incompressible flow. The numerical results show high accuracy and efficiency.