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- 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)

This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are… (More)

- 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)

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D… (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, Jordi Blasco
- Numerische Mathematik
- 2000

- Santiago Badia, Ramon Codina, Ramon Planas
- J. Comput. Physics
- 2013

Various multifield problems and among them fluid-structure interaction applications arise in nearly all fields of engineering. The present work contributes to the development of a stable and robust approach for the numerical simulation of fluid-structure interaction problems. In particular two-dimensional and three-dimensional elastic structues interacting… (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 ≤ Cδt with C uniform with respect to h and δt. Standard residual-based… (More)

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

In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented falls within the category of fixed-grid methods. Even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed-grid… (More)