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In this paper we analyze a stabilized finite element method to approximate the convection-diffusion equation on moving domains using an arbitrary Lagrangian Eulerian (ALE) framework. As basic numerical strategy, we discretize the equation in time using first and second order backward differencing (BDF) schemes, whereas space is discretized using a… (More)

In this work, a stabilized formulation to solve the inductionless magnetohydrodynamic (MHD) problem using the finite element (FE) method is presented. The MHD problem couples the Navier-Stokes and a Darcy-type problem for the electric potential via Lorentz's force in the momentum equation of the Navier-Stokes equations and the currents generated by the… (More)

In this paper we propose stabilized finite element methods for both Stokes' and Darcy's problems that accommodate any interpolation of velocities and pressures. Apart from the interest of this fact, the important issue is that we are able to deal with both problems at the same time, in a completely unified manner, in spite of the fact that the functional… (More)

In this article we analyze some residual-based stabilization techniques for the transient Stokes problem when considering anisotropic time-space discretizations. We define an anisotropic time-space discretization as a family of time-space partitions that does not satisfy the condition h 2 ≤ Cδt with C uniform with respect to h and δt. Standard… (More)

A new mixed finite element approximation of Maxwell's problem is proposed, its main features being that it is based on a novel augmented formulation of the continuous problem and the introduction of a mesh dependent stabilizing term, which yields a very weak control on the divergence of the unknown. The method is shown to be stable and convergent in the… (More)

Variational multiscale methods lead to stable finite element approximations of the Navier-Stokes equations, both dealing with the indefinite nature of the system (pressure stability) and the velocity stability loss for high Reynolds numbers. These methods enrich the Galerkin formulation with a sub-grid component that is modeled. In fact, the effect of the… (More)