A two-level finite element method for time-dependent incompressible Navier-Stokes equations with non-smooth initial data

Abstract

In this article, we analyze a two-level finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size $H$ and solving a Stokes problem on a fine grid of size $h,h<<H$. This method gives optimal convergence for velocity in $H^1$-norm and for pressure in $L^2$-norm. The analysis takes in to account the loss of regularity of the solution at $t=0$ of the Navier-Stokes equations.

References in corpus (3)

• Static two-grid mixed finite-element approximations to the Navier-Stokes equations
• Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
• A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations

Cited by in corpus (1)

• Optimal error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data