The long-time behavior of finite element solutions of semilinear parabolic problems

Prof. Stig Larsson

Department of Mathematics, Chalmers University of Technology and G\"oteborg University, G\"oteborg (Sweden)

The solutions of a system of reaction-diffusion equations (semilinear parabolic PDEs) may be viewed as a dynamical system in an infinite-dimensional phase space. A perturbed dynamical system is obtained when the solutions are approximated by a numerical method. It is then interesting to know to what extent the dynamics of the perturbed dynamical system reflects the dynamics of the original one. I will review some results of this type concerning, e.g., convergence of attractors and local behavior near hyperbolic fixed points.