Attractors of set-valued partial differential equations under discretization

The approximation of the global attractor of a dissipative set-valued reaction-diffusion equation is investigated when a Galerkin approximation is used to obtain a finite-dimensional inclusion equation, to which the linear implicit Euler scheme is then applied. The existence and upper semicontinuous convergence of the various attractors with decreasing time step and increasing dimension are established. The equivalence of the attractors with those of the corresponding convexified systems is also shown.