Data assimilation in 2D nonlinear advection diffusion equations, using an explicit stabilized leapfrog scheme run backward in time

Abstract

With an artificial example of a 2D nonlinear advection diffusion equation on the unit square this paper considers the data assimilation problem of finding initial values that can evolve into a close approximation to a desired target result at some realistic T > 0. Highly non smooth target data are considered, that may not correspond to actual solutions at time T, and it may not be possible to find such initial values. The aim is to illustrate the inherent difficulties of the ill-posed data assimilation problem.