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Documents published in Scipedia

Anisotropic adaptive meshing and monolithic variational multiscale method for fluid-structure interaction
E. Hachem, S. Feghali, R. Codina, T. Coupez

Computers and Structures (2013). Vol. 122, pp. 88-100

Abstract
This paper presents a monolithic formulation framework combined with an anisotropic mesh adaptation for fluid–structure interaction (FSI) applications with complex geometry. The fluid–solid interfaces are captured using a level-set method. A new a posteriori error estimate, based on the length distribution tensor approach and the associated edge based error analysis, is then used to ensure an accurate capturing of the discontinuities at the fluid–solid interface. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of edges in the mesh. The presence of the structure will be taken into account by means of an extra stress tensor in the Navier–Stokes equations. The system is solved using a stabilized three-field, stress, velocity and pressure finite element (FE) formulation. It consists in the decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales and also in the efficient enrichment of the extra constraint. We assess the accuracy of the proposed formulation by simulating 2D and 3D time-dependent numerical examples such as: falling disk in a channel, turbulent flows behind an airfoil profile and flow behind an immersed vehicle.
Abstract
This paper presents a monolithic formulation framework combined with an anisotropic mesh adaptation for fluid–structure interaction (FSI) applications with complex geometry. [...]
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A variational multiscale method with subscales on the element boundaries for the Helmholtz equation
J. Baiges, R. Codina

Int. J. Numer. Meth. Engng. (2013). Vol. 93 (6), pp. 664-684

Abstract
In this paper, we apply the variational multiscale method with subgrid scales on the element boundaries to the problem of solving the Helmholtz equation with low‐order finite elements. The expression for the subscales is obtained by imposing the continuity of fluxes across the interelement boundaries. The stabilization parameter is determined by performing a dispersion analysis, yielding the optimal values for the different discretizations and finite element mesh configurations. The performance of the method is compared with that of the standard Galerkin method and the classical Galerkin least‐squares method with very satisfactory results. Some numerical examples illustrate the behavior of the method.
Abstract
In this paper, we apply the variational multiscale method with subgrid scales on the element boundaries to the problem of solving the Helmholtz equation with low‐order finite [...]
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On unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics
S. Badia, R. Codina, R. Planas

Journal of Computational Physics (2013). Vol. 234, pp. 399-416

Abstract
In this work, we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation is the fact that it always converges to the physical solution, even for singular ones. A detailed set of numerical experiments have been performed in order to validate our approach.
Abstract
In this work, we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this [...]
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A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes
J. Baiges, R. Codina, F. Henke, S. Shahmiri, W. Wall

Int. J. Numer. Meth. Engng. (2012). Vol. 90 (5), pp. 636-658

Abstract
In this paper, we propose a way to weakly prescribe Dirichlet boundary conditions in embedded finite element meshes. The key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation, relatively small, and can be fixed a priori. Moreover, the formulation is symmetric for symmetric problems. An additional element‐discontinuous stress field is used to enforce the boundary conditions in the Poisson problem. Additional terms are required in order to guarantee stability in the convection–diffusion equation and the Stokes problem. The proposed method is then easily extended to the transient Navier–Stokes equations.
Abstract
In this paper, we propose a way to weakly prescribe Dirichlet boundary conditions in embedded finite element meshes. The key feature of the method is that the algorithmic [...]
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A third‐order velocity correction scheme obtained at the discrete level
H. Owen, R. Codina

Int. J. Numer. Meth. Fluids (2012). Vol. 69 (1), pp. 52-72

Abstract
In this work we explore a velocity correction method that introduces the splitting at the discrete level. In order to do so, the algebraic continuity equation is transformed into a discrete pressure Poisson equation and a velocity extrapolation is used. In Badia et al. (IJNMF, 2008, p. 351), where the method was introduced, the discrete Laplacian that appears in the pressure Poisson equation is approximated by a continuous one using an extrapolation for the pressure. In this work we explore the possibility of actually solving the discrete Laplacian. This introduces significant differences because the pressure extrapolation is avoided and only a velocity extrapolation is needed. Our numerical results indicate that it is the second‐order pressure extrapolation which makes third‐order methods unstable. Instead, second‐order velocity extrapolations do not lead to instabilities. Avoiding the pressure extrapolation allows to obtain stable solutions in problems that become unstable when the Laplacian is approximated. A comparison with a pressure correction scheme is also presented to verify the well‐known fact that the use of a second order pressure extrapolation leads to instabilities. Therefore we conclude that it is the combination of a velocity correction scheme with a discrete Laplacian that allows to obtain a stable third‐order scheme by avoiding the pressure extrapolation.
Abstract
In this work we explore a velocity correction method that introduces the splitting at the discrete level. In order to do so, the algebraic continuity equation is transformed [...]
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A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions
S. Badia, R. Codina

SIAM J. Numer. Anal. (2012). Vol. 50 (2), pp. 398-417

Abstract
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 natural H(curl 0; Ω) norm for this unknown. In particular, convergence also applies to singular solutions, for which classical nodal-based interpolations are known to suffer from spurious convergence upon mesh refinement.
Abstract
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 [...]
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Stokes, Maxwell and Darcy: A single finite element approximation for three model problems
S. Badia, R. Codina

Applied Numerical Mathematics (2012). Vol. 62 (4) pp. 246-263

Abstract
In this work we propose stabilized finite element methods for Stokesʼ, Maxwellʼs and Darcyʼs problems that accommodate any interpolation of velocities and pressures. We briefly review the formulations we have proposed for these three problems independently in a unified manner, stressing the advantages of our approach. In particular, for Darcyʼs problem we are able to design stabilized methods that yield optimal convergence both for the primal and the dual problems. In the case of Maxwellʼs problem, the formulation we propose allows one to use continuous finite element interpolations that converge optimally to the continuous solution even if it is non-smooth. Once the formulation is presented for the three model problems independently, we also show how it can be used for a problem that combines all the operators of the independent problems. Stability and convergence is achieved regardless of the fact that any of these operators dominates the others, a feature not possible for the methods of which we are aware.
Abstract
In this work we propose stabilized finite element methods for Stokesʼ, Maxwellʼs and Darcyʼs problems that accommodate any interpolation of velocities and pressures. We [...]
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A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem
S. Badia, R. Codina

Applied Mathematics and Computation (2011). Vol. 218 (8), pp. 4276-4294

Abstract
Continuous Galerkin formulations are appealing due to their low computational cost, whereas discontinuous Galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters. Since many electromagnetic problems involve materials with different physical properties, this last point is very important. For this reason, in this article we have developed a combined cG–dG formulation for Maxwell’s problem that allows arbitrary finite element spaces with functins continuous in patches of finite elements and discontinuous on the interfaces of these patches. In particular, the second formulation we propose comes from a novel continuous Galerkin formulation that reduces the amount of stabilization introduced in the numerical system. In all cases, we have performed stability and convergence analyses of the methods. The outcome of this work is a new approach that keeps the low CPU cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones. All these methods have been tested using a problem with singular solution and another one with different materials, in order to prove that in fact the resulting formulations can properly deal with these problems.
Abstract
Continuous Galerkin formulations are appealing due to their low computational cost, whereas discontinuous Galerkin formulation facilitate adaptative mesh refinement and are [...]
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The Fixed‐Mesh ALE approach for the numerical simulation of floating solids
J. Baiges, R. Codina, H. Coppola-Owen

Int. J. Numer. Meth. Fluids (2011). Vol. 67 (8), pp. 1004-1023

Abstract
In this paper, we propose a method to solve the problem of floating solids using always a background mesh for the spatial discretization of the fluid domain. The main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian–Eulerian framework, the distinctive characteristic being that at each time step results are projected onto a fixed, background mesh. We pay special attention to the tracking of the various interfaces and their intersections, and to the approximate imposition of coupling conditions between the solid and the fluid.
Abstract
In this paper, we propose a method to solve the problem of floating solids using always a background mesh for the spatial discretization of the fluid domain. The main feature [...]
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Finite element dynamical subgrid-scale approximation of low Mach number flow equations
M. Ávila, J. Principe, R. Codina

Journal of Computational Physics (2011). Vol. 230, pp. 7988-8009

Abstract
In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier Stokes equations in the small Mach number. In contrast to the commonly used Boussinesq approximation, this model permits to take volumetric deformation into account. Although the former is more general than the later, both systems have similar mathematical structure and their numerical approximation can suffer the same type of instabilities. We propose a stabilized finite element approximation based on the the variational multiscale method, in which a decomposition of the approximating space into a coarse scale resolvable part and a fine scale subgrid part is performed. Modeling the subscale and taking its effect on the coarse scale problem into account, results in a stable formulation. The quality of the final approximation (accuracy, efficiency) depends on the particular model. The distinctive features of our approach are to consider the subscales as transient and to keep the scale splitting in all the nonlinear terms. The first ingredient permits to obtain an improved time discretization scheme (higher accuracy, better stability, no restrictions on the time step size). The second ingredient permits to prove global conservation properties. It also allows us to approach the problem of dealing with thermal turbulence from a strictly numerical point of view. Numerical tests show that nonlinear and dynamic subscales give more accurate solutions than classical stabilized methods.
Abstract
In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number [...]
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Articles (Documents not available in Scipedia)

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows
O Colomés, S Badia, R Codina, J Principe

Computer Methods in Applied Mechanics and Engineering 285, 32-63, 2015
Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
M Cervera, M Chiumenti, L Benedetti, R Codina

Computer Methods in Applied Mechanics and Engineering 285, 752-775, 2015
Large eddy simulation of low mach number flows using dynamic and orthogonal subgrid scales
M Avila, R Codina, J Principe

Computers & Fluids 99, 44-66, 2014
Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity
E Castillo, R Codina

Computer Methods in Applied Mechanics and Engineering 279, 554-578, 2014
Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem
E Castillo, R Codina

Computer Methods in Applied Mechanics and Engineering 279, 579-605, 2014
Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid–structure interaction
E Hachem, S Feghali, R Codina, T Coupez

Computers & Structures 122, 88-100, 2013
On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics
S Badia, R Codina, R Planas

Journal of Computational Physics 234, 399-416, 2013
Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation
E Hachem, S Feghali, R Codina, T Coupez

International Journal for Numerical Methods in Engineering 94 (9), 805-825, 2013
Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations
J Baiges, R Codina, S Idelsohn

International Journal for Numerical Methods in Fluids 72 (12), 1219-1243, 2013
Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows
O Guasch, R Codina

Computer Methods in Applied Mechanics and Engineering 261, 154-166, 2013
Stokes, Maxwell and Darcy: A single finite element approximation for three model problems
S Badia, R Codina

Applied Numerical Mathematics 62 (4), 246-263, 2012
A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions
S Badia, R Codina

SIAM Journal on Numerical Analysis 50 (2), 398-417, 2012
A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes
J Baiges, R Codina, F Henke, S Shahmiri, WA Wall

International Journal for Numerical Methods in Engineering 90 (5), 636-658, 2012
Approximation of the inductionless MHD problem using a stabilized finite element method
R Planas, S Badia, R Codina

Journal of Computational Physics 230 (8), 2977-2996, 2011
The Fixed‐Mesh ALE approach for the numerical simulation of floating solids
J Baiges, R Codina, H Coppola‐Owen

International Journal for Numerical Methods in Fluids 67 (8), 1004-1023, 2011
A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations
M Avila, J Principe, R Codina

Journal of Computational Physics 230 (22), 7988-8009, 2011
Mesh objective modeling of cracks using continuous linear strain and displacement interpolations
M Cervera, M Chiumenti, R Codina

International Journal for Numerical Methods in Engineering 87 (10), 962-987, 2011
On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes
J Principe, R Codina

Computer methods in applied mechanics and engineering 199 (21), 1386-1402, 2010
Long-term stability estimates and existence of a global attractor in a finite element approximation of the Navier–Stokes equations with numerical subgrid scale modeling
S Badia, R Codina, JV Gutiérrez-Santacreu

SIAM Journal on Numerical Analysis 48 (3), 1013-1037, 2010
Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling
R Codina, J Principe, M Ávila

International Journal of Numerical Methods for Heat & Fluid Flow 20 (5), 492-516, 2010
The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems
J Baiges, R Codina

International journal for numerical methods in engineering 81 (12), 1529-1557, 2010
Stabilized continuous and discontinuous Galerkin techniques for Darcy flow
S Badia, R Codina

Computer Methods in Applied Mechanics and Engineering 199 (25), 1654-1667, 2010
The dissipative structure of variational multiscale methods for incompressible flows
J Principe, R Codina, F Henke

Computer Methods in Applied Mechanics and Engineering 199 (13), 791-801, 2010
Mixed stabilized finite element methods in nonlinear solid mechanics: Part ii: Strain localization
M Cervera, M Chiumenti, R Codina

Computer Methods in Applied Mechanics and Engineering 199 (37), 2571-2589, 2010
Mathematical models for thermally coupled low speed flows
J Principe, R Codina

Advances in Theoretical and Applied Mechanics 2 (2), 93-112, 2009
Subscales on the element boundaries in the variational two-scale finite element method
R Codina, J Principe, J Baiges

Computer Methods in Applied Mechanics and Engineering 198 (5), 838-852, 2009
Finite element approximation of the three-field formulation of the Stokes problem using arbitrary interpolations
R Codina

SIAM Journal on Numerical Analysis 47 (1), 699-718, 2009
Approximate imposition of boundary conditions in immersed boundary methods
R Codina, J Baiges

International Journal for Numerical Methods in Engineering 80 (11), 1379-1405, 2009
On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space–time discretization
S Badia, R Codina

Applied Mathematics and Computation 207 (2), 415-433, 2009
The fixed-mesh ALE approach for the numerical approximation of flows in moving domains
R Codina, G Houzeaux, H Coppola-Owen, J Baiges

Journal of Computational Physics 228 (5), 1591-1611, 2009
Unified stabilized finite element formulations for the Stokes and the Darcy problems
S Badia, R Codina

SIAM journal on Numerical Analysis 47 (3), 1971-2000, 2009
A stabilized finite element approximation of low speed thermally coupled flows
J Principe, R Codina

International Journal of Numerical Methods for Heat & Fluid Flow 18 (7/8 ..., 2008
Finite element approximation of the modified Boussinesq equations using a stabilized formulation
R Codina, JM González‐Ondina, G Díaz‐Hernández, J Principe

International Journal for Numerical Methods in Fluids 57 (9), 1249-1268, 2008
Finite element approximation of the hyperbolic wave equation in mixed form
R Codina

Computer Methods in Applied Mechanics and Engineering 197 (13), 1305-1322, 2008
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales
R Codina

Applied Numerical Mathematics 58 (3), 264-283, 2008
An algebraic subgrid scale finite element method for the convected Helmholtz equation in two dimensions with applications in aeroacoustics
O Guasch, R Codina

Computer Methods in Applied Mechanics and Engineering 196 (45), 4672-4689, 2007
A finite element model for free surface flows on fixed meshes
AH Coppola‐Owen, R Codina

International Journal for Numerical Methods in Fluids 54 (10), 1151-1171, 2007
Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition
S Badia, R Codina

Numerische Mathematik 107 (4), 533-557, 2007
On some fluid–structure iterative algorithms using pressure segregation methods. Application to aeroelasticity
S Badia, R Codina

International Journal for Numerical Methods in Engineering 72 (1), 46-71, 2007
Algebraic pressure segregation methods for the incompressible Navier-Stokes equations
S Badia, R Codina

Archives of Computational Methods in Engineering 15 (3), 1-52, 2007
Dynamic subscales in the finite element approximation of thermally coupled incompressible flows
R Codina, J Principe

International journal for numerical methods in fluids 54 (6‐8), 707-730, 2007
A finite element method for the solution of rotary pumps
G Houzeaux, R Codina

Computers & Fluids 36 (4), 667-679, 2007
Time dependent subscales in the stabilized finite element approximation of incompressible flow problems
R Codina, J Principe, O Guasch, S Badia

Computer Methods in Applied Mechanics and Engineering 196 (21), 2413-2430, 2007
Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations
R Codina, H Coppola‐Owen, P Nithiarasu, CB Liu

International Journal for Numerical Methods in Engineering 66 (10), 1672-1689, 2006
On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems
R Codina, S Badia

Computer Methods in Applied Mechanics and Engineering 195 (23), 2900-2918, 2006
Stabilized finite element approximation of the stationary magneto-hydrodynamics equations
R Codina, N Hernández-Silva

Computational Mechanics 38 (4-5), 344-355, 2006
Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ALE framework
S Badia, R Codina

SIAM Journal on Numerical Analysis 44 (5), 2159-2197, 2006
The Characteristic‐Based Split (CBS) scheme—a unified approach to fluid dynamics
P Nithiarasu, R Codina, OC Zienkiewicz

International Journal for Numerical Methods in Engineering 66 (10), 1514-1546, 2006
Improving Eulerian two‐phase flow finite element approximation with discontinuous gradient pressure shape functions
AH Coppola‐Owen, R Codina

International journal for numerical methods in fluids 49 (12), 1287-1304, 2005
A finite element model for the simulation of lost foam casting
G Houzeaux, R Codina

International journal for numerical methods in fluids 46 (2), 203-226, 2004
A stabilized finite element predictor–corrector scheme for the incompressible Navier–Stokes equations using a nodal‐based implementation
R Codina, A Folch

International Journal for Numerical Methods in Fluids 44 (5), 483-503, 2004
Error estimates for an operator-splitting method for incompressible flows
J Blasco, R Codina

Applied Numerical Mathematics 51 (1), 1-17, 2004
Approximation of the incompressible Navier–Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes
R Codina, O Soto

Computer Methods in Applied Mechanics and Engineering 193 (15), 1403-1419, 2004
An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems
G Houzeaux, R Codina

Journal of Computational and Applied Mathematics 158 (2), 243-276, 2003
A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations
G Houzeaux, R Codina

Computer Methods in Applied Mechanics and Engineering 192 (31), 3343-3377, 2003
A numerical model to track two‐fluid interfaces based on a stabilized finite element method and the level set technique
R Codina, O Soto

International Journal for Numerical Methods in Fluids 40 (1‐2), 293-301, 2002
CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter
R Codina, OC Zienkiewicz

International Journal for Numerical Methods in Biomedical Engineering 18 (2 ..., 2002
Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales
R Codina, J Blasco

Computing and Visualization in Science 4 (3), 167-174, 2002
Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
R Codina

Computer Methods in Applied Mechanics and Engineering 191 (39), 4295-4321, 2002
Transmission conditions with constraints in finite element domain decomposition methods for flow problems
G Houzeaux, R Codina

International Journal for Numerical Methods in Biomedical Engineering 17 (3 ..., 2001
Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier–Stokes equations
J Blasco, R Codina

Applied Numerical Mathematics 38 (4), 475-497, 2001
Implementation of a stabilized finite element formulation for the incompressible Navier–Stokes equations based on a pressure gradient projection
R Codina, J Blasco, GC Buscaglia, A Huerta

International Journal for Numerical Methods in Fluids 37 (4), 419-444, 2001
A stabilized finite element method for generalized stationary incompressible flows
R Codina

Computer Methods in Applied Mechanics and Engineering 190 (20), 2681-2706, 2001
Pressure stability in fractional step finite element methods for incompressible flows
R Codina

Journal of Computational Physics 170 (1), 112-140, 2001
A nodal‐based implementation of a stabilized finite element method for incompressible flow problems
R Codina

International Journal for numerical methods in fluids 33 (5), 737-766, 2000
Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection
GC Buscaglia, FG Basombrio, R Codina

International journal for numerical methods in fluids 34 (1), 65-92, 2000
Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations
R Codina, J Blasco

Numerische Mathematik 87 (1), 59-81, 2000
On stabilized finite element methods for linear systems of convection–diffusion-reaction equations
R Codina

Computer Methods in Applied Mechanics and Engineering 188 (1), 61-82, 2000
Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection
R Codina, J Blasco

Computer Methods in Applied Mechanics and Engineering 182 (3), 277-300, 2000
Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
R Codina

Computer methods in applied mechanics and engineering 190 (13), 1579-1599, 2000
Numerical solution of the incompressible Navier–Stokes equations with Coriolis forces based on the discretization of the total time derivative
R Codina

Journal of Computational Physics 148 (2), 467-496, 1999
Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows
R Codina, O Soto

International journal for numerical methods in fluids 30 (3), 309-333, 1999
The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems
OC Zienkiewicz, P Nithiarasu, R Codina, M Vazquez, P Ortiz

International Journal for Numerical Methods in Fluids 31 (1), 359-392, 1999
A numerical model for temporal variations during explosive central vent eruptions
A Folch, J Martí, R Codina, M Vazquez

Journal of Geophysical Research: Solid Earth 103 (B9), 20883-20899, 1998
Shock capturing viscosities for the general fluid mechanics algorithm
P Nithiarasu, OC Zienkiewicz, BVK Sai, K Morgan, R Codina, M Vazquez

International Journal for Numerical Methods in Fluids 28 (9), 1325-1353, 1998
A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm
J Blasco Lorente, R Codina, A Huerta

International Journal for Numerical Methods in Fluids 28 (10), 1391-1419, 1998
A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form
R Codina, M Vázquez, OC Zienkiewicz

International Journal for Numerical Methods in Fluids 27 (1‐4), 13-32, 1998
Comparison of some finite element methods for solving the diffusion-convection-reaction equation
R Codina

Computer Methods in Applied Mechanics and Engineering 156 (1-4), 185-210, 1998
Finite element solution of the Stokes problem with dominating Coriolis force
R Codina, O Soto

Computer Methods in Applied Mechanics and Engineering 142 (3-4), 215-234, 1997
A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation
R Codina, J Blasco

Computer Methods in Applied Mechanics and Engineering 143 (3-4), 373-391, 1997
Block-iterative algorithms for nonlinear coupled problems.
M Cervera, R Codina

CIMNE, 1996
SPLIT, CHARACTERISTIC BASED SEMI‐IMPLICIT ALGORITHM FOR LAMINAR/TURBULENT INCOMPRESSIBLE FLOWS
OC Zienkiewicz, BVK Satya Sai, K Morgan, R Codina

International Journal for Numerical Methods in Fluids 23 (8), 787-809, 1996
On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled problems
M Cervera, R Codina, M Galindo

Engineering computations 13 (6), 4-30, 1996
A general algorithm for compressible and incompressible flow—Part II. Tests on the explicit form
OC Zienkiewicz, K Morgan, BVK Sai, R Codina, M Vasquez

International Journal for Numerical Methods in Fluids 20 (8‐9), 887-913, 1995
A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
OC Zienkiewicz, R Codina

International Journal for Numerical Methods in Fluids 20 (8‐9), 869-885, 1995
Mould filling simulation using finite elements
R Codina, U Schäfer, E Oñate

International Journal of Numerical Methods for Heat & Fluid Flow 4 (4), 291-310, 1994
Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space
R Codina

International journal for numerical methods in engineering 36 (9), 1445-1464, 1993
An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations
R Codina

Computer methods in applied mechanics and engineering 110 (3-4), 237-262, 1993
A finite element formulation for the numerical solution of the convection-diffusion equation
R Codina

Centro Internacional de Métodos Numéricos en Ingeniería, 1993
A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
R Codina

Computer Methods in Applied Mechanics and Engineering 110 (3-4), 325-342, 1993
A finite element model for incompressible flow problems
R Codina

Universitat Politècnica de Catalunya, 1992
The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements
R Codina, E Oñate, M Cervera

Computer Methods in Applied Mechanics and Engineering 94 (2), 239-262, 1992

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Articles (Documents not available in Scipedia)

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Large eddy simulation of low mach number flows using dynamic and orthogonal subgrid scales

Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid–structure interaction

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations

Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows

Stokes, Maxwell and Darcy: A single finite element approximation for three model problems

A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions

A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes

Approximation of the inductionless MHD problem using a stabilized finite element method

The Fixed‐Mesh ALE approach for the numerical simulation of floating solids

A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations

Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes

Long-term stability estimates and existence of a global attractor in a finite element approximation of the Navier–Stokes equations with numerical subgrid scale modeling

Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling

The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems

Stabilized continuous and discontinuous Galerkin techniques for Darcy flow

The dissipative structure of variational multiscale methods for incompressible flows

Mixed stabilized finite element methods in nonlinear solid mechanics: Part ii: Strain localization

Mathematical models for thermally coupled low speed flows

Subscales on the element boundaries in the variational two-scale finite element method

Finite element approximation of the three-field formulation of the Stokes problem using arbitrary interpolations

Approximate imposition of boundary conditions in immersed boundary methods

On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space–time discretization

The fixed-mesh ALE approach for the numerical approximation of flows in moving domains

Unified stabilized finite element formulations for the Stokes and the Darcy problems

A stabilized finite element approximation of low speed thermally coupled flows

Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Finite element approximation of the hyperbolic wave equation in mixed form

Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

An algebraic subgrid scale finite element method for the convected Helmholtz equation in two dimensions with applications in aeroacoustics

A finite element model for free surface flows on fixed meshes

Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition

On some fluid–structure iterative algorithms using pressure segregation methods. Application to aeroelasticity

Algebraic pressure segregation methods for the incompressible Navier-Stokes equations

Dynamic subscales in the finite element approximation of thermally coupled incompressible flows

A finite element method for the solution of rotary pumps

Time dependent subscales in the stabilized finite element approximation of incompressible flow problems

Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations

On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems

Stabilized finite element approximation of the stationary magneto-hydrodynamics equations

Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ALE framework

The Characteristic‐Based Split (CBS) scheme—a unified approach to fluid dynamics

Improving Eulerian two‐phase flow finite element approximation with discontinuous gradient pressure shape functions

A finite element model for the simulation of lost foam casting

A stabilized finite element predictor–corrector scheme for the incompressible Navier–Stokes equations using a nodal‐based implementation

Error estimates for an operator-splitting method for incompressible flows

Approximation of the incompressible Navier–Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes

An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems

A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations

A numerical model to track two‐fluid interfaces based on a stabilized finite element method and the level set technique

CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter

Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales

Stabilized finite element approximation of transient incompressible flows using orthogonal subscales

Transmission conditions with constraints in finite element domain decomposition methods for flow problems

Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier–Stokes equations

Implementation of a stabilized finite element formulation for the incompressible Navier–Stokes equations based on a pressure gradient projection

A stabilized finite element method for generalized stationary incompressible flows

Pressure stability in fractional step finite element methods for incompressible flows

A nodal‐based implementation of a stabilized finite element method for incompressible flow problems

Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection

Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations

On stabilized finite element methods for linear systems of convection–diffusion-reaction equations

Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection

Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods

Numerical solution of the incompressible Navier–Stokes equations with Coriolis forces based on the discretization of the total time derivative

Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows

The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems

A numerical model for temporal variations during explosive central vent eruptions

Shock capturing viscosities for the general fluid mechanics algorithm

A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm

A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form