Javier de Frutos

TL;DR: Taking into account the loss of regularity suffered by the solution of the Navier–Stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data, error bounds of order O(h2)$\mathcal O( h^{2})$ in space are proved.

TL;DR: In this article, a transboundary pollution differential game where pollution control is spatially distributed among a number of agents with predetermined spatial relationships is analyzed, and the authors evaluate the impact of the strategic and spatially dynamic behaviour of the agents on the design of equilibrium environmental policies.

TL;DR: The main goal is to prove that adding a grad-div stabilization term to the Galerkin approximation has a stabilizing effect for small viscosity, and error bounds are obtained that do not depend on the inverse of the Viscosity in the case where the solution is sufficiently smooth.

TL;DR: In this article, an approximation of the time-dependent Oseen problem using inf-sup stable mixed finite elements in a Galerkin method with grad-div stabilization is studied.

TL;DR: This procedure improves the order of convergence for the approximations to the velocity and the pressure and choice of a discrete pressure space endowed with an inf-sup condition independent of the discretization parameter leads to optimal error bounds for the pressure.