M. Braack, T. Richter. Stabilized finite elements for 3D reactive flows. Int. J. Numer. Meth. Fluids 51(9-10) (2006) DOI 10.1002/fld.1160
R. Codina, J. Blasco, G. Buscaglia, A. Huerta. Implementation of a stabilized finite element formulation for the incompressible Navier-Stokes equations based on a pressure gradient projection. Int. J. Numer. Meth. Fluids 37(4) (2001) DOI 10.1002/fld.182
P. Nadukandi, E. Oñate, J. Garcia. Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements. Int. J. Numer. Meth. Fluids 57(9) DOI 10.1002/fld.1863
E. Oñate, P. Nadukandi, S. Idelsohn, J. García, C. Felippa. A family of residual-based stabilized finite element methods for Stokes flows. Int. J. Numer. Meth. Fluids 65(1-3) (2010) DOI 10.1002/fld.2468
E. Hachem, T. Kloczko, H. Digonnet, T. Coupez. Stabilized finite element solution to handle complex heat and fluid flows in industrial furnaces using the immersed volume method. Int. J. Numer. Meth. Fluids 68(1) (2010) DOI 10.1002/fld.2498
R. Codina, O. Soto. A numerical model to track two-fluid interfaces based on a stabilized finite element method and the level set technique. Int. J. Numer. Meth. Fluids 40(1-2) (2002) DOI 10.1002/fld.277
R. Rossi, A. Larese, P. Dadvand, E. Oñate. An efficient edge-based level set finite element method for free surface flow problems. Int. J. Numer. Meth. Fluids 71(6) (2012) DOI 10.1002/fld.3680
Y. Zhang, F. Pin, S. Yim. A heterogeneous flow model based on DD method for free surface fluid-structure interaction problems. Int. J. Numer. Meth. Fluids 74(4) (2013) DOI 10.1002/fld.3852
C. Bayona, J. Baiges, R. Codina. Variational multiscale approximation of the one-dimensional forced Burgers equation: The role of orthogonal subgrid scales in turbulence modeling. Int J Numer Meth Fluids 86(5) (2017) DOI 10.1002/fld.4420
J. Sari, F. Cremonesi, M. Khalloufi, F. Cauneau, P. Meliga, Y. Mesri, E. Hachem. Anisotropic adaptive stabilized finite element solver for RANS models. Int J Numer Meth Fluids 86(11) (2017) DOI 10.1002/fld.4475
F. Salazar, J. Irazábal, A. Larese, E. Oñate. Numerical modelling of landslide-generated waves with the particle finite element method (PFEM) and a non-Newtonian flow model. Int. J. Numer. Anal. Meth. Geomech. 40(6) (2015) DOI 10.1002/nag.2428
T. Coupez, H. Digonnet, E. Hachem, P. Laure, L. Silva, R. Valette. Multidomain Finite Element Computations. (2013) DOI 10.1002/9781118557884.ch5
D. Irisarri, G. Hauke. Stabilized virtual element methods for the unsteady incompressible Navier–Stokes equations. Calcolo 56(4) (2019) DOI 10.1007/s10092-019-0332-5
E. Burman. Robust error estimates in weak norms for advection dominated transport problems with rough data. Math. Models Methods Appl. Sci. 24(13) (2014) DOI 10.1142/s021820251450033x
O. GUASCH, R. CODINA. COMPUTATIONAL AEROACOUSTICS OF VISCOUS LOW SPEED FLOWS USING SUBGRID SCALE FINITE ELEMENT METHODS. J. Comp. Acous. 17(03) (2011) DOI 10.1142/s0218396x09003975
S. Badia, R. Codina. Algebraic pressure segregation methods for the incompressible Navier-Stokes equations. ARCO 15(3) DOI 10.1007/bf03024946
A. Belver, A. Iban, R. Rossi. Lock-in and drag amplification effects in slender line-like structures through CFD. Wind and Structures An International Journal 15(3) DOI 10.12989/was.2012.15.3.189
R. Codina, J. Baiges. Weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non-matching meshes. Int. J. Numer. Meth. Engng 104(7) (2014) DOI 10.1002/nme.4815
G. Scovazzi, B. Carnes, X. Zeng, S. Rossi. A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach. Int. J. Numer. Meth. Engng 106(10) (2015) DOI 10.1002/nme.5138
N. Abboud, G. Scovazzi. Elastoplasticity with linear tetrahedral elements: A variational multiscale method. Int J Numer Methods Eng 115(8) (2018) DOI 10.1002/nme.5831
S. Badia, R. Codina. Analysis of a Stabilized Finite Element Approximation of the Transient Convection‐Diffusion Equation Using an ALE Framework. SIAM J. Numer. Anal. 44(5) DOI 10.1137/050643532
R. Codina. Finite Element Approximation of the Three-Field Formulation of the Stokes Problem Using Arbitrary Interpolations. SIAM J. Numer. Anal. 47(1) DOI 10.1137/080712726
S. Badia, R. Codina. Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems. SIAM J. Numer. Anal. 47(3) DOI 10.1137/08072632x
E. Burman, A. Ern, M. Fernández. Explicit Runge–Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems. SIAM J. Numer. Anal. 48(6) DOI 10.1137/090757940
S. Badia, R. Codina, J. Gutiérrez-Santacreu. 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. SIAM J. Numer. Anal. 48(3) DOI 10.1137/090766681
S. Badia, R. Codina, H. Espinoza. Stability, Convergence, and Accuracy of Stabilized Finite Element Methods for the Wave Equation in Mixed Form. SIAM J. Numer. Anal. 52(4) DOI 10.1137/130918708
S. Badia, A. Hierro. On Monotonicity-Preserving Stabilized Finite Element Approximations of Transport Problems. SIAM J. Sci. Comput. 36(6) DOI 10.1137/130927206
E. Burman. Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part II: Hyperbolic Equations. SIAM J. Sci. Comput. 36(4) DOI 10.1137/130931667
E. Burman, F. Schieweck. Local CIP Stabilization for Composite Finite Elements. SIAM J. Numer. Anal. 54(3) DOI 10.1137/15m1039390
E. Burman. A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty. SIAM J. Numer. Anal. 43(5) DOI 10.1137/s0036142903437374
A. Allendes, F. Durán, R. Rankin. Error estimation for low-order adaptive finite element approximations for fluid flow problems. IMA J Numer Anal 36(4) (2015) DOI 10.1093/imanum/drv031
G. Li, D. Peterseim, M. Schedensack. Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions. 38(3) (2017) DOI 10.1093/imanum/drx027
G. Barrenechea, E. Castillo, R. Codina. Time-dependent semidiscrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilized formulation. 39(2) (2018) DOI 10.1093/imanum/dry018
J. Rojek, E. Oñate, R. Taylor. CBS-based stabilization in explicit solid dynamics. Int. J. Numer. Meth. Engng 66(10) DOI 10.1002/nme.1689
E. Oñate, S. Idelsohn, C. Felippa. Consistent pressure Laplacian stabilization for incompressible continua via higher-order finite calculus. Int. J. Numer. Meth. Engng. 87(1-5) (2010) DOI 10.1002/nme.3021
B. Schrefler, R. Codina, F. Pesavento, J. Principe. Thermal coupling of fluid flow and structural response of a tunnel induced by fire. Int. J. Numer. Meth. Engng. 87(1-5) (2010) DOI 10.1002/nme.3077
I. Caylak, R. Mahnken. Stabilization of mixed tetrahedral elements at large deformations. Int. J. Numer. Meth. Engng 90(2) (2011) DOI 10.1002/nme.3320
P. Sváček. On Higher-Order Space-Time Discretization of an Nonlinear Aeroelastic Problem with the Consideration of Large Displacements. (2012) DOI 10.1007/978-3-642-33134-3_63
J. San Mauro, F. Salazar, M. Toledo, F. Caballero, C. Ponce-Farfán, T. Ramos. Modelación física y numérica de aliviaderos en laberinto con fondo poliédrico. ing.agua 20(3) (2016) DOI 10.4995/ia.2016.4614
P. Becker, S. Idelsohn. A multiresolution strategy for solving landslides using the Particle Finite Element Method. Acta Geotech. 11(3) (2016) DOI 10.1007/s11440-016-0464-6
C. Yang, J. Samper. A Subgrid-Scale Stabilized Finite Element Method for Multicomponent Reactive Transport through Porous Media. Transp Porous Med 78(1) (2008) DOI 10.1007/s11242-008-9288-7
T. Chacón Rebollo, M. Gómez Mármol, M. Restelli. Numerical Analysis of Penalty Stabilized Finite Element Discretizations of Evolution Navier–Stokes Equations. J Sci Comput 63(3) (2014) DOI 10.1007/s10915-014-9918-x
E. Oñate, R. Taylor, O. Zienkiewicz, J. Rojek. A residual correction method based on finite calculus. Engineering Computations 20(5/6) DOI 10.1108/02644400310488790
S. Rodolfo Idelsohn, N. Marcelo Nigro, J. Marcelo Gimenez, R. Rossi, J. Marcelo Marti. A fast and accurate method to solve the incompressible Navier‐Stokes equations. Engineering Computations 30(2) DOI 10.1108/02644401311304854
O. Soto, R. Löhner, F. Camelli. A linelet preconditioner for incompressible flow solvers. Int Jnl of Num Meth for HFF 13(1) DOI 10.1108/09615530310456796
J. Principe, R. Codina. A stabilized finite element approximation of low speed thermally coupled flows. Int Jnl of Num Meth for HFF 18(7/8) DOI 10.1108/09615530810898980
E. Hachem, H. Digonnet, E. Massoni, T. Coupez. Immersed volume method for solving natural convection, conduction and radiation of a hat‐shaped disk inside a 3D enclosure. Int Jnl of Num Meth for HFF 22(6) DOI 10.1108/09615531211244871
E. Moreno, M. Cervera. Elementos finitos mixtos estabilizados para flujos confinados de Bingham y de Herschel-Bulkley. ParteI: Formulación. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 32(2) DOI 10.1016/j.rimni.2015.02.004
N. Lafontaine, R. Rossi, M. Cervera, M. Chiumenti. Formulación mixta estabilizada explícita de elementos finitos para sólidos compresibles y quasi-incompresibles. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 33(1-2) DOI 10.1016/j.rimni.2015.09.003
N. Lafontaine, M. Cervera, R. Rossi, M. Chiumenti. Una formulación mixta estabilizada explícita para plasticidad con localización de deformaciones. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 33(3-4) DOI 10.1016/j.rimni.2016.06.001
Y. Zhang, S. Yim. Solitary Wave Breaking on Irregular 3D Bathymetry Using a Coupled Potential + Viscous Flow Model. J. Eng. Mech. 141(6) DOI 10.1061/(asce)em.1943-7889.0000894
L. Tobiska. Recent Results on Local Projection Stabilization for Convection-Diffusion and Flow Problems. (2009) DOI 10.1007/978-3-642-00605-0_4
G. Houzeaux, B. Eguzkitza, M. Vázquez. A variational multiscale model for the advection-diffusion-reaction equation. Commun. Numer. Meth. Engng. 25(7) DOI 10.1002/cnm.1156
D. Einstein, F. Del Pin, X. Jiao, A. Kuprat, J. Carson, K. Kunzelman, R. Cochran, J. Guccione, M. Ratcliffe. Fluid-structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future. Int. J. Numer. Meth. Biomed. Engng. 26(3-4) DOI 10.1002/cnm.1280
P. Sánchez, V. Sonzogni, A. Huespe. Study of a stabilized mixed finite element with emphasis on its numerical performance for strain localization problems. Commun. Numer. Meth. Engng. 24(4) (2007) DOI 10.1002/cnm.969
P. Sváček. Numerical approximations of flow induced vibrations of vocal folds. EPJ Web Conf. 143 (2017) DOI 10.1051/epjconf/201714302123
M. Braack. A stabilized finite element scheme for the Navier-Stokes equations on quadrilateral anisotropic meshes. ESAIM: M2AN 42(6) (2008) DOI 10.1051/m2an:2008032
P. Knobloch, L. Tobiska. Improved stability and error analysis for a class of local projection stabilizations applied to the Oseen problem. Numer. Methods Partial Differential Eq. 29(1) (2012) DOI 10.1002/num.21706
G. LUBE, G. RAPIN. RESIDUAL-BASED STABILIZED HIGHER-ORDER FEM FOR A GENERALIZED OSEEN PROBLEM. Math. Models Methods Appl. Sci. 16(07) (2011) DOI 10.1142/s0218202506001418
F. Del Pin, C. Huang, I. Çaldichoury, R. Paz. On the performance and accuracy of PFEM-2 in the solution of biomedical benchmarks. Comp. Part. Mech. 7(1) (2019) DOI 10.1007/s40571-019-00241-4
L. Marioni, M. Khalloufi, F. Bay, E. Hachem. Two-fluid flow under the constraint of external magnetic field. Int Jnl of Num Meth for HFF 27(11) DOI 10.1108/hff-09-2016-0371
C. Bayona Roa, J. Baiges, R. Codina. Variational multi-scale finite element approximation of the compressible Navier-Stokes equations. Int Jnl of Num Meth for HFF 26(3/4) DOI 10.1108/hff-11-2015-0483
P. Sváček, J. Horáček. Numerical Simulation of Glottal Flow in Interaction with Self Oscillating Vocal Folds: Comparison of Finite Element Approximation with a Simplified Model. Commun. comput. phys. 12(3) (2015) DOI 10.4208/cicp.011010.280611s
P. Sánchez, V. Sonzogni, A. Huespe, J. Oliver. Stabilized Mixed Finite Elements With Embedded Strong Discontinuities for Shear Band Modeling. 73(6) (2006) DOI 10.1115/1.2190233
M. Chiumenti, C. Agelet de Saracibar, M. Cervera. On the Numerical Modeling of the Thermomechanical Contact for Metal Casting Analysis. 130(6) (2008) DOI 10.1115/1.2897923
H. Roos. Robust Numerical Methods for Singularly Perturbed Differential Equations: A Survey Covering 2008–2012. ISRN Applied Mathematics 2012 DOI 10.5402/2012/379547
S. Feghali, E. Hachem, T. Coupez. Monolithic stabilized finite element method for rigid body motions in the incompressible Navier-Stokes flow. European Journal of Computational Mechanics 19(5-7) (2012) DOI 10.3166/ejcm.19.547-573
T. Chacón Rebollo, R. Lewandowski. A Projection-Based Variational Multiscale Model. (2014) DOI 10.1007/978-1-4939-0455-6_11
T. Chacón Rebollo, R. Lewandowski. Finite Element Approximation of the Steady Smagorinsky Model. (2014) DOI 10.1007/978-1-4939-0455-6_9
T. Chacón Rebollo, S. Fernández-García. On the computation of the stabilized coefficients for the 1D spectral VMS method. SeMA 75(4) (2018) DOI 10.1007/s40324-018-0153-5
R. Codina. On hp convergence of stabilized finite element methods for the convection–diffusion equation. SeMA 75(4) (2018) DOI 10.1007/s40324-018-0154-4
A. Antunes, P. Lyra, R. Willmersdorf, S. Bastos. An implicit monolithic formulation based on finite element formulation for incompressible Navier–Stokes equations. J Braz. Soc. Mech. Sci. Eng. 37(1) (2014) DOI 10.1007/s40430-014-0155-x
R. Reyes, R. Codina, J. Baiges, S. Idelsohn. Reduced order models for thermally coupled low Mach flows. Adv. Model. and Simul. in Eng. Sci. 5(1) (2018) DOI 10.1186/s40323-018-0122-7
R. Codina. Finite Element Approximation of the Convection-Diffusion Equation: Subgrid-Scale Spaces, Local Instabilities and Anisotropic Space-Time Discretizations. (2011) DOI 10.1007/978-3-642-19665-2_10
P. Sváček, J. Horáček. Numerical Approximation of Flow Induced Vibration of Vocal Folds. (2011) DOI 10.1007/978-3-642-19665-2_24
P. Sváček, J. Valášek. Mathematical modelling and numerical simulation of flow induced vibrations of vocal folds model with collisions. DOI 10.1063/1.5113987
A. Gooneie, S. Schuschnigg, C. Holzer. A Review of Multiscale Computational Methods in Polymeric Materials. Polymers 9(12) (2017) DOI 10.3390/polym9010016
S. Badia, R. Codina. Algebraic Pressure Segregation Methods for the Incompressible Navier-Stokes Equations. Arch Computat Methods Eng 15(3) (2008) DOI 10.1007/s11831-008-9020-3
C. de Saracibar, M. Chiumenti, M. Cervera, N. Dialami, A. Seret. Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes. Arch Computat Methods Eng 21(1) (2014) DOI 10.1007/s11831-014-9094-z
A. Larese, R. Rossi, E. Oñate. Finite Element Modeling of Free Surface Flow in Variable Porosity Media. Arch Computat Methods Eng 22(4) (2014) DOI 10.1007/s11831-014-9140-x
S. Marras, J. Kelly, M. Moragues, A. Müller, M. Kopera, M. Vázquez, F. Giraldo, G. Houzeaux, O. Jorba. A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin. Arch Computat Methods Eng 23(4) (2015) DOI 10.1007/s11831-015-9152-1
N. Ahmed, T. Chacón Rebollo, V. John, S. Rubino. A Review of Variational Multiscale Methods for the Simulation of Turbulent Incompressible Flows. Arch Computat Methods Eng 24(1) (2015) DOI 10.1007/s11831-015-9161-0
M. Andre, K. Bletzinger, R. Wüchner. A complementary study of analytical and computational fluid-structure interaction. Comput Mech 55(2) (2014) DOI 10.1007/s00466-014-1104-3
P. Becker, S. Idelsohn, E. Oñate. A unified monolithic approach for multi-fluid flows and fluid–structure interaction using the Particle Finite Element Method with fixed mesh. Comput Mech 55(6) (2014) DOI 10.1007/s00466-014-1107-0
N. Lafontaine, R. Rossi, M. Cervera, M. Chiumenti. Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics. Comput Mech 55(3) (2015) DOI 10.1007/s00466-015-1121-x
M. Cervera, N. Lafontaine, R. Rossi, M. Chiumenti. Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity. Comput Mech 58(3) (2016) DOI 10.1007/s00466-016-1305-z
M. Cervera, G. Barbat, M. Chiumenti. Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy. Comput Mech 60(5) (2017) DOI 10.1007/s00466-017-1438-8
I. Iaconeta, A. Larese, R. Rossi, E. Oñate. A stabilized mixed implicit Material Point Method for non-linear incompressible solid mechanics. Comput Mech 63(6) (2018) DOI 10.1007/s00466-018-1647-9
E. Karabelas, G. Haase, G. Plank, C. Augustin. Versatile stabilized finite element formulations for nearly and fully incompressible solid mechanics. Comput Mech 65(1) (2019) DOI 10.1007/s00466-019-01760-w