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Barrenechea, Gabriel and Castillo, Ernesto and Pacheco, Douglas (2024) Implicit-explicit schemes for incompressible flow problems with variable viscosity. SIAM Journal on Scientific Computing, 46 (4). A2660-A2682. ISSN 1064-8275

Amiri, Abdolreza and Barrenechea, Gabriel R. and Pryer, Tristan (2024) A nodally bound-preserving finite element method for reaction-convection-diffusion equations. Mathematical Models and Methods in Applied Sciences, 34 (08). pp. 1533-1565. ISSN 0218-2025

Barrenechea, Gabriel R. and Georgoulis, Emmanuil H. and Pryer, Tristan and Veeser, Andreas (2024) A nodally bound-preserving finite element method. IMA Journal of Numerical Analysis, 44 (4). 2198–2219. ISSN 0272-4979

Barrenechea, Gabriel R. and Gomes, Antonio Tadeu A. and Paredes, Diego (2024) A multiscale hybrid method. SIAM Journal on Scientific Computing, 46 (3). A1628 - A1657. ISSN 1064-8275

Barrenechea, Gabriel R and Burman, Erik and Cáceres, Ernesto and Guzmán, Johnny (2024) Continuous interior penalty stabilization for divergence-free finite element methods. IMA Journal of Numerical Analysis, 44 (2). pp. 980-1002. drad030. ISSN 0272-4979

Barrenechea, Gabriel R. and John, Volker and Knobloch, Petr (2024) Finite element methods respecting the discrete maximum principle for convection-diffusion equations. SIAM Review, 66 (1). pp. 3-88. ISSN 0036-1445

Barrenechea, Gabriel R. and Süli, Endre (2023) Analysis of a stabilised finite element method for power-law fluids. Constructive Approximation, 57 (2). pp. 295-325. ISSN 0176-4276

Allendes, Alejandro and Barrenechea, Gabriel R. and Novo, Julia (2021) A divergence-free stabilized finite element method for the evolutionary Navier-Stokes equations. SIAM Journal on Scientific Computing, 43 (6). A3809–A3836. ISSN 1064-8275

Ahmed, Naveed and Barrenechea, Gabriel R. and Burman, Erik and Guzmán, Johnny and Linke, Alexander and Merdon, Christian (2021) A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation. SIAM Journal on Numerical Analysis, 59 (5). 2746–2774. ISSN 0036-1429

Barrenechea, Gabriel and Burman, Erik and Guzman, Johnny (2020) Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow. Mathematical Models and Methods in Applied Sciences, 30 (5). pp. 847-865. ISSN 0218-2025

Barrenechea, Gabriel R. and Jaillet, Fabrice and Paredes, Diego and Valentin, Frédéric (2020) The multiscale hybrid mixed method in general polygonal meshes. Numerische Mathematik, 145 (1). pp. 197-237. ISSN 0029-599X

Pascarella, G. and Fossati, M. and Barrenechea, G. (2019) Impact of POD modes energy redistribution on flow reconstruction for unsteady flows of impulsively started airfoils and wings. International Journal of Computational Fluid Dynamics. ISSN 1029-0257

Barrenechea, Gabriel R and Wachtel, Andreas (2019) The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes. IMA Journal of Numerical Analysis. ISSN 0272-4979

Barrenechea, Gabriel R. and Castillo, Ernesto and Codina, Ramon (2019) Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation. IMA Journal of Numerical Analysis, 39 (2). 792–819. ISSN 0272-4979

Barrenechea, Gabriel R. and John, Volker and Knobloch, Petr and Rankin, Richard (2018) A unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations. SeMA Journal, 75 (4). 655–685. ISSN 2281-7875

Allendes, Alejandro and Barrenechea, Gabriel R. and Narranjo, Cesar (2018) A divergence-free low-order stabilized finite element method for a generalized steady state Boussinesq problem. Computer Methods in Applied Mechanics and Engineering, 340. pp. 90-120. ISSN 0045-7825

Barrenechea, Gabriel R. and Poza, Abner H. and Yorston, Heather (2018) A stabilised finite element method for the convection-diffusion-reaction equation in mixed form. Computer Methods in Applied Mechanics and Engineering, 339. pp. 389-415. ISSN 0045-7825

Barrenechea, Gabriel R. and Bosy, Michał and Dolean, Victorita (2018) Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations. ETNA - Electronic Transactions on Numerical Analysis, 49. pp. 41-63. ISSN 1068-9613

Barrenechea, Gabriel R. and Bosy, Michał and Dolean, Victorita and Nataf, Frédéric and Tournier, Pierre Henri (2018) Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem. Computational Methods in Applied Mathematics. ISSN 1609-9389

Barrenechea, Gabriel R. and Gonzalez Aguayo, Cheherazada (2018) A stabilised finite element method for a fictitious domain problem allowing small inclusions. Numerical Methods for Partial Differential Equations, 34 (1). pp. 167-183. ISSN 0749-159X

Allendes, Alejandro and Barrenechea, Gabriel R. and Rankin, Richard (2017) Fully computable error estimation of a nonlinear, positivity-preserving discretization of the convection-diffusion-reaction equation. SIAM Journal on Scientific Computing, 39 (5). A1903–A1927. ISSN 1064-8275

Barrenechea, Gabriel and Knobloch, Petr (2017) Analysis of a group finite element formulation. Applied Numerical Mathematics, 118. pp. 238-248. ISSN 0168-9274

Barrenechea, Gabriel and Wachtel, Andreas (2017) Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes. ESAIM: Mathematical Modelling and Numerical Analysis. ISSN 0764-583X (In Press)

Barrenechea, Gabriel and Burman, Erik and Karakatsani, Fotini (2017) Blending low-order stabilised finite element methods : a positivity-preserving local projection method for the convection-diffusion equation. Computer Methods in Applied Mechanics and Engineering, 317. pp. 1169-1193. ISSN 0045-7825

Barrenechea, Gabriel R. and Volker, John and Knobloch, Petr (2017) An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes. Mathematical Models and Methods in Applied Sciences, 27 (3). pp. 525-548. ISSN 0218-2025

Barrenechea, Gabriel R. and Burman, Erik and Karakatsani, Fotini (2017) Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes. Numerische Mathematik, 135 (2). pp. 521-545. ISSN 0029-599X

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2016) Analysis of algebraic flux correction schemes. SIAM Journal on Numerical Analysis, 54 (4). 2427–2451. ISSN 0036-1429

Barrenechea, Gabriel and Boulton, Lyonell and Boussaid, Nabile (2016) Local two-sided bounds for eigenvalues of self-adjoint operators. Numerische Mathematik. ISSN 0029-599X

Ainsworth, Mark and Barrenechea, Gabriel R. and Wachtel, Andreas (2015) Stabilisation of high aspect ratio mixed finite elements for incompressible flow. SIAM Journal on Numerical Analysis, 53 (2). 1107–1120. ISSN 0036-1429

Barrenechea, Gabriel R. and Barrios, Tomás P. and Wachtel, Andreas (2014) Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model. Calcolo. ISSN 0008-0624

Barrenechea, G. R. and Boulton, L. and Boussaid, N. (2014) Finite element Eigenvalue enclosures for the Maxwell operator. SIAM Journal on Scientific Computing, 36 (6). A2887–A2906. ISSN 1064-8275

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2014) Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension. IMA Journal of Numerical Analysis. ISSN 0272-4979

Barrenechea, Gabriel and Volker, John and Knobloch, Petr (2013) A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis, 47 (5). pp. 1335-1366. ISSN 0764-583X

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2013) On the adaptive selection of the parameter in stabilized finite element approximations. SIAM Journal on Numerical Analysis, 51 (3). pp. 1585-1609. ISSN 0036-1429

Barrenechea, Gabriel R. and Chouly, Franz (2012) A local projection stabilized method for fictitious domains. Applied Mathematics Letters, 25 (12). pp. 2071-2076. ISSN 0893-9659

Ainsworth, Mark and Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Rankin, Richard Andrew Robert (2012) Computable error bounds for nonconfirming Fortin-Soulie finite element approximation of the Stokes problem. IMA Journal of Numerical Analysis, 32 (2). pp. 414-447. ISSN 0272-4979

Araya, Rodolfa and Barrenechea, Gabriel R. and Poza, Abner H. and Valentin, Frédéric (2012) Convergence analysis of a residual local projection method for the Navier-Stokes equation. SIAM Journal on Numerical Analysis, 50 (2). pp. 669-699. ISSN 0036-1429

Allendes Flores, Alejandro Ignacio and Barrenechea, Gabriel and Hernández, Erwin and Valentin, Frédéric (2011) A two-level enriched finite element method for a mixed problem. Mathematics of Computation, 80. pp. 11-41. ISSN 0025-5718

Barrenechea, Gabriel and Valentin, Frédéric (2011) Beyond pressure stabilization : a low-order local projection method for the Oseen equation. International Journal for Numerical Methods in Engineering, 86 (7). 801–815. ISSN 0029-5981

Araya, Rodolfa and Barrenechea, Gabriel and Jaillet, Fabrice and Rodriguez, Rodolfo (2011) Finite-element analysis of a static fluid–solid interaction problem. IMA Journal of Numerical Analysis, 31 (3). pp. 886-913. ISSN 0272-4979

Barrenechea, Gabriel and Valentin, Frédéric (2010) A residual local projection method for the Oseen equation. Computer Methods in Applied Mechanics and Engineering, 199 (29-32). pp. 1906-1921.

Barrenechea, Gabriel and Valentin, Frédéric (2010) Consistent local projection stabilized finite element methods. SIAM Journal on Numerical Analysis, 48 (5). pp. 1801-1825. ISSN 0036-1429

Araya, Rodolfo and Barrenechea, Gabriel R. and Franca, Leopoldo P. and Valentin, Frédéric (2009) Stabilization arising from PGEM : a review and further developments. Applied Numerical Mathematics, 59 (9). pp. 2065-2081. ISSN 0168-9274

Barrenechea, Gabriel R. and Chouly, Franz (2009) A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations. Zeitschrift fur Angewandte Mathematik und Mechanik, 89 (1). pp. 54-68. ISSN 0044-2267

Barrenechea, G. R. and Franca, L. P. and Valentin, F. (2009) A symmetric nodal conservative finite element method for the Darcy equation. SIAM Journal on Numerical Analysis, 47 (5). pp. 3652-3677. ISSN 0036-1429

Araya, Rodolfo and Barrenechea, Gabriel R. and Poza, Abner (2008) An adaptive stabilized finite element method for the generalized Stokes problem. Journal of Computational and Applied Mathematics, 214 (2). pp. 457-479. ISSN 0377-0427

Barrenechea, Gabriel and Blasco, Jordi (2007) Pressure stabilization of finite element approximations of time-dependent incompressible flow problems. Computer Methods in Applied Mechanics and Engineering, 197 (1-4). pp. 219-231.

Araya, Rodolfa and Barrenechea, Gabriel and Valentin, Frédéric (2007) A stabilized finite-element method for the Stokes problem including element and edge residuals. IMA Journal of Numerical Analysis, 27 (1). pp. 172-197. ISSN 0272-4979

Barrenechea, G.R. and Franca, L.P. and Valentin, F. (2007) A Petrov-Galerkin enriched method: a mass conservative finite element method for the Darcy equation. Journal of Sound and Vibration, 196 (21-24). pp. 2449-2464. ISSN 0022-460X

Araya, Rodolfo and Barrenechea, Gabriel R. and Valentin, Frédéric (2006) Stabilized finite element methods based on multiscale enrichment for the Stokes problem. SIAM Journal on Numerical Analysis, 44 (1). 322–348. ISSN 0036-1429

Barrenechea, Gabriel and Valentin, Frédéric (2005) Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem. Comptes Rendus Mathematique, 341 (10). pp. 635-640.

Barrenechea, Gabriel R. and Le Tallec, Patrick and Valentin, Frédéric (2002) New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains. ESAIM: Mathematical Modelling and Numerical Analysis, 36 (2). pp. 177-203. ISSN 0764-583X

Barrenechea, G.R. and Valentin, F. (2002) An unusual stabilized finite element method for a generalized Stokes problem. Numerische Mathematik, 92 (4). pp. 653-677. ISSN 0029-599X

Book Section

Barrenechea, Gabriel R. and Bosy, Michał and Dolean, Victorita; Sherwin, Spencer J. and Peiró, Joaquim and Vincent, Peter E. and Moxey, David and Schwab, Christoph, eds. (2020) Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions. In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, 134 . Springer-Verlag, Cham, Switzerland, pp. 179-189. ISBN 978-3-030-39646-6

Barrenechea, Gabriel R. and Wachtel, Andreas; Knobloch, Petr, ed. (2016) A note on the stabilised Q1-P0 method on quadrilaterals with high aspect ratios. In: Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014. Lecture Notes in Computational Science and Engineering, 108 . Springer-Verlag, CZE, pp. 1-11. ISBN 9783319257259