Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation
Friday 9th September 2016
Antonietti, P.F.; Merlet, B.; Morgan, P.; Verani, M.
We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated with the discretization is non-increasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Lojasiewicz-Simon inequality.