Rigorous numerical integration of PDEs by means of Finite Element Method

I will present the results on the attractor structure for problems governed by PDEs. I will demonstrate that the approach based on rigorous numerical simulations and Finite Element Method makes it possible to find the trajectories in the global attractor. As an example I will present the proof of the periodic orbit existence for periodically forced Burgers equation and Dirichlet conditions. 

The results were obtained jointly with Piotr Zgliczyński.