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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)

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)

In this paper we present a numerical formulation to solve thermally coupled MHD flows. It is a stabilized finite element method, whose design is based on splitting the unknown into a finite element component and a subscale and on giving an approximation for the latter. The main features of the formulation are that it allows to use equal interpolation for… (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)

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)

The stress-displacement-pressure formulation of the elasticity problem may suffer from two types of numerical instabilities related to the finite element interpolation of the unknowns. The first is the classical pressure instability that occurs when the solid is incompressible, whereas the second is the lack of stability in the stresses. To overcome these… (More)