We introduce a technique to compute exact anelastic sensitivity kernels in the time domain
using parsimonious disk storage. The method is based on a reordering of the time loop of …

In this article, we prove that data assimilation by feedback nudging can be achieved for the
three-dimensional quasi-geostrophic equation in a simplified scenario using only large …

An artificial example of a coupled system of three nonlinear partial differential equations
generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well …

The diffusive back-and-forth nudging (DBFN) is an easy-to-implement iterative data
assimilation method based on the well-known nudging method. It consists of a sequence of …

In this paper, we are interested in designing and analyzing a finite element data assimilation
method for laminar steady flow described by the linearized incompressible Navier–Stokes …

This paper constructs an unconditionally stable explicit finite difference scheme, marching
backward in time, that can solve an interesting but limited class of ill-posed, time-reversed …

This paper constructs an unconditionally stable explicit difference scheme, marching
backward in time, that can solve a limited, but important class of time-reversed 2D Burgers' …

Richardson's leapfrog scheme is notoriously unconditionally unstable in well-posed,
forward, linear dissipative evolution equations. Remarkably, that scheme can be stabilized …

The 2D viscous Burgers equation is a system of two nonlinear equations in two unknowns, u
(x, y, t), v (x, y, t). This paper considers the data assimilation problem of finding initial values …

We investigate a state estimation problem for an infinite dimensional system appearing in
population dynamics. More precisely, given a linear model for age-structured populations …