A nonlinear local projection-based finite element method for unsteady Navier-Stokes equations

Abstract:

In this study, a stable local projection finite element method is derived for unsteady Navier-Stokes equations. This method is formed by local projection of advection term and pressure gradient. By using the equal-order conforming finite elements in space and implicit finite difference scheme in time, we derive a full discrete formulation and prove the stability and convergence of the approximation solution. Notably, the error estimates hold even for large Reynolds numbers.