Parameter identification and state estimation for linear parabolic equations - Sergiy Zhuk

Abstract

In this talk I will present an extension of Galerkin projection method for linear evolution equations in abstract Hilbert space. Specifically, I will discuss a closure of Galerkin projection method for linear parabolic equations on bounded convex domains and structure preserving time descretization based on Mobious variational integrators. The method will be illustrated by numerical examples: tracking of a discharged pollutant slick in a 2D fluid and hydraulic diffusivity inversion for a confined aquifer modelled by 2D Darcy equations.  Experimental  results for the identification of the 2D fluid flow displayed on a given sequence of satellite images may be presented as well.