Title.  Going mobile: if Pete Towns(h)end were to do data assimilation

Speaker.  Mike Jolly, Indiana University Bloomington, IN

Abstract.  We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations on the torus. We prove that, for any error threshold, if the reference flow is analytic with sufficiently large analyticity radius, then it can be recovered within that threshold.  Numerical computations are included to demonstrate the effectiveness of this approach, as well as variants with data on moving subdomains.  We prove that, if the movement is fast enough, then the algorithm perfectly synchronizes with a reference solution. The analysis suggests an informed scheme in which the subdomain moves according to a region where the error is dominant is optimal.   Numerical simulations are presented that compare the efficacy of movement that follows a regular pattern, one guided by the dominant error, and one that is random.