CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

6 avril 2021 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Rigorous FEM based forward in time integration of dissipative PDEs

Séminaire par Piotr Kalita (Jagiellonian University, Poland)

We present the technique for computer assisted rigorous forward in time integration of problems governed by dissipative PDEs. The approach is based on the Finite Element Method. The key concepts lie in the propagation of the a priori energy estimates needed to bound the infinite dimensional remainder and in rigorous integration of differential inclusions. The technique is illustrated by the computer assisted construction of the time periodic solution for periodically forced one-dimensional Burgers equation with homogeneous Dirichlet boundary conditions. Talk is based on joint work with Piotr Zgliczyński.