# Preprint des Projektes: DFG Forschergruppe Spektrale Analysis, asymptotische Verteilungen und stochastische Prozesse

## Numerische Approximation und Spektrale Analysis unendlich-dimensionaler Dynamischer Systeme

04-013 Wolf-Jürgen Beyn, Vasiliy S. Kolezhuk, Sergei Pilyugin.
Convergence of discretized attractors for parabolic equations on the line

We show that, for a semilinear parabolic equation on the real line satisfying a dissipativity condition, global attractors of time-space discretizations converge (with respect to the Hausdorff semi-distance) to the attractor of the continuous system as the discretization steps tend to zero. The attractors considered correspond to pairs of function spaces (in the sense of Babin-Vishik) with weighted and locally uniform norms (taken from Mielke-Schneider) used for both the continuous and the discrete system.