Asymptotics of Numerical Methods for Nonlinear Evolution Equations

We consider the evolution equation (E) du/dt = au + f(t,u), u(0) = u0 in a Hilbert space H, where A is assumed to generate a C0 semigroup. The asymptotic-in-time behavior of solutions to (E) is studied together with the asymptotic-in-time behavior of methods for approximating (E).