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- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2006

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)

- Ramon Planas, Santiago Badia, Ramon Codina
- J. Comput. Physics
- 2011

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)

- Ramon Codina, Jordi Blasco
- Numerische Mathematik
- 2000

- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2009

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 paper we analyse a pressure stabilized, nite element method for the unsteady, incompressible Navier{Stokes equations in primitive variables; for the time discretization we focus on a fully implicit, monolithic scheme. We provide some error estimates for the fully discrete solution which show that the velocity is rst order accurate in the time step… (More)

SUMMARY In this paper we suggest some algorithms for the fluid-structure interaction problem stated using a domain decomposition framework. These methods involve stabilized pressure segregation methods for the solution of the fluid problem and fixed point iterative algorithms for the fluid-structure coupling. With one single loop the solution of the coupled… (More)

- Santiago Badia, Ramon Codina
- Applied Mathematics and Computation
- 2009

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)

- Santiago Badia, Ramon Codina
- SIAM J. Numerical Analysis
- 2012

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)

- Ramon Codina, Guillaume Houzeaux, Herbert Coppola-Owen, Joan Baiges
- J. Comput. Physics
- 2009