The exponential dichotomy on general approximation scheme (Q376151)

This paper is interested in the numerical analysis of abstract parabolic problems with a hyperbolic generator. The general approach to establish a discrete dichotomy in the case of discrete approximation in space and time is shown. The authors use the theory of compact approximations and show that the phase space in the neighborhood of the hyperbolic equilibrium under rather general approximation schemes can be splitted similarly as in the continuous case. Particularly, this can be shown for the operators with compact resolvents and condensing semigroups and the finite element as well as finite difference methods.