Long-time Convergence of Fully Discrete Nonlinear Galerkin Method——Case of Finite-elements

We apply an abstract framwork introduced by the authors, to study the long time behaviour of a fully discrete nonlinear Galerkin method which is integrated by a Runge Kutta method in time, and give error estimates uniform in time, under the basic assumption that the continuous solution is asymptotically exponentially stable. We discuss reaction diffusion equation, Navier Stokes equation and Cahn Hilliard equation respectively.