This paper is dedicated to a new way of presenting the Tikhonov regularization in the form of
a mixed formulation. Such formulation is well adapted to the regularization of linear ill-posed …

We consider a stabilized finite element method based on a spacetime formulation, where the
equations are solved on a global (unstructured) spacetime mesh. A unique continuation …

The aim of this work is to present some strategies to solve numerically controllability
problems for the two-dimensional heat equation, the Stokes equations and the Navier …

We consider a finite element discretization for the reconstruction of the final state of the heat
equation, when the initial data is unknown, but additional data is given in a sub domain in …

We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy
problem, or other related data assimilation problems. The method has a local conservation …

We are interested in solving the unique continuation problem for the heat equation, ie, we
want to reconstruct the solution of the heat equation in a target space-time subdomain given …

We design a primal-dual stabilized finite element method for the numerical approximation of
a data assimilation problem subject to the acoustic wave equation. For the forward problem …

Data assimilation combines control theory and scientific computing to propose a set of
methods for coupling dynamic models and data sequences for estimation and prediction in …

This paper delves into addressing an inverse Cauchy problem using the primal-dual
method. This approach is motivated by the inherent challenges posed by the irregular nature …

We present a fully discrete finite element method for the interior null controllability problem
subject to the wave equation. For the numerical scheme, piecewise affine continuous …