The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a St...

It was shown recently by Su et al. (2016) that Nesterov's accelerated gradient method for minimizing a smooth convex function $f$ can be thought of as the time discretization second-order ODE, and $f(x(t))$ converges to its optimal value at rate $\mathcal{O}(1/t^2)$ along any trajectory $x(t)$ this ODE. A variational formulation introduced in Wibisono which allowed convergence $\mathcal{O}(1/t^...