Rigorous FEM based forward in time integration of dissipative PDEs

Abstract: 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.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

Series comments: To have access to the zoom details of the talks, please register at www.crm.math.ca/camp-nonlinear