December 13 – Maxime Breden: An introduction to a posteriori validation techniques, illustrated on the Navier-Stokes equations

Maxime Breden: Thursday 13 December at 11 am, A415 Inria Paris.
The aim of a posteriori validation techniques is to obtain mathematically rigorous and quantitative existence theorems, using numerical simulations. Given an approximate solution, the general strategy is to combine a posteriori estimates with analytical ones to apply a fixed point theorem, which then yields the existence of a true solution in an explicit neighborhood of the approximate one.
In the first part of the talk, I’ll present the main ideas in more detail, and describe the general framework in which they are applicable. In the second part, I’ll then focus on a specific example and explain how to validate a posteriori periodic solutions of the Navier-Stokes equations with a Taylor-Green type of forcing. This is joint work with Jan Bouwe van den Berg, Jean-Philippe Lessard and Lennaert van Veen.

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