A class of Lagrangian continuous dynamical systems with set-valued controller and subjected to a perturbation force has been thoroughly studied in [3]. In this paper, we study the time discretization of these set-valued ...

Adaptive finite element methods (FEMs) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. ...

We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Kačanov iteration and a mesh adaptation step is performed after each linear solve. The ...

Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter ...

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society. We study the behavior of the trajectories of a second-order differential equation with vanishing damping, governed by the ...

An exact projection method for the numerical solution of the incompressible Navier–Stokes equations is devised. In all spatial discretizations, fourth-order compact finite differences are used, including domain boundaries ...

In this work we propose a numerical strategy to solve a family of partial differential equations arising from the water-wave theory. These problems may contain four terms; a source which is an algebraic function of the ...