Articles in refereed journals

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56. Audusse, E., Barrenechea, G.R., Decoene, A., and Quemar, P. : Stability analysis of a finite element approximation for the Navier-Stokes equation with free surface.

ESAIM:M2AN,  58 (1), 107–130, (2024).

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55. Barrenechea, G.R., John, V., and Knobloch, P.: Finite element methods respecting the discrete maximum principle for convection-diffusion equations.

SIAM Review, 66 (1), 3–88, (2024).

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54. Barrenechea, G.R. and Suli, E.: Analysis of a stabilised finite element method for power-law fluids.

Constructive Approximation, 57, 295–325 (2023).

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53. Allendes, A., Barrenechea, G.R., and Novo, J. : A divergence-free stabilised finite element method for the evolutionary Navier--Stokes equations.

SIAM Journal on Scientific Computing, 43(6), A3809-A3836, (2021).

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52. AHMEED, N., BARRENECHEA, G.R., BURMAN, E., GUZMAN, J., LINKE, A., and Merdon, C.: A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation.

SIAM Journal on Numerical Analysis, (5), 2746-2774, (2021).

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51. BARRENECHEA, G.R. and WACHTEL, A.:

The inf-sup stability of the lowest order Taylor-Hood pair on anisotropic meshes.

IMA Journal of Numerical Analysis, 40(4), 2377-2398, (2020).

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50. BARRENECHEA, G.R., BURMAN, E., and GUZMAN, J.:

Well-posedness and H(div)- conforming finite element approximation of a linearised model for inviscid incompressible flow.

M3AS, 30(5), 847-865, (2020) .

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49. BARRENECHEA, G.R., PAREDES, D., JAILLET, F., and VALENTIN, F.:

The Multiscale Hybrid Mixed method in general polygonal meshes.

Numerische Mathematik, 145(1),197–237, (2020).

 

48 PASCARELLA, G., FOSSATI, M., and BARRENECHEA, G.R. :

Impact of POD modes energy redistribution on flow reconstruction for unsteady flows of impulsively started airfoils and wings.

International Journal of Computational Fluid Dynamics, 34(2), 108-118, (2020).

 

47. BARRENECHEA, G.R., BOSY, M., DOLEAN, V., NATAF, F. and TOURNIER, P.-H.:

Hybrid discontinuous Galerkin discretisation and preconditioning of the Stokes problem with non standard boundary conditions.

Computational Methods in Applied Mathematics, 19(4), 703-722, (2019).

 

46. PASCARELLA, G., FOSSATI, M., and BARRENECHEA, G.R. :

Adaptive Reduced Basis Method for the Reconstruction of Unsteady Vortex-dominated Flows.

Computers and Fluids, 190 , 382–397, (2019).

 

45. BARRENECHEA, G.R., CASTILLO, E., and CODINA, R.:

Time-dependent semi-discrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilised formulation.

IMA J. Numer. Anal., 39(2), 792–819, (2019).

 

44. BARRENECHEA, G.R., JOHN, V., KNOBLOCH, P., and RANKIN, R.:

A unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations.

Boletın de la Sociedad Espanola de Matematica Aplicada : SeMA Journal, 75, 655-685, (2018).

 

43. ALLENDES, A., BARRENECHEA, G.R., and NARANJO, C.:

A divergence-free low-order stabilized finite element method for the steady state Boussinesq problem.

Computer Methods in Applied Mechanics and Engineering, Vol. 340, 90–120, (2018).

 

42. BARRENECHEA, G.R., POZA, A., and YORSTON, H.:

A stabilised finite element method for the convection-diffusion-reaction equation in mixed form.

Computer Methods in Applied Mechanics and Engineering, Vol. 339, 389–415, (2018).

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41. BARRENECHEA, G.R., and WACHTEL, A.:

Stabilised finite element methods for the Oseen problem on anisotropic quadrilateral meshes.

ESAIM:M2AN, Vol. 52, 99–122, (2018).

 

40. BARRENECHEA, G.R., BOSY, M. and DOLEAN, V.:

Numerical assessment of two-level domain decomposition preconditioners for incompressible Stokes and elasticity equations.

Electronic Transactions on Numerical Analysis, Vol. 49, 41 – 63, (2018).

 

39. BARRENECHEA, G.R. and GONZALEZ, C.:

A stabilized finite element method for a fictitious domain problem allowing small inclusions. Numerical Methods for Partial Differential Equations, Vol. 34,(1), 167-183, (2018).

 

38. ALLENDES, A., BARRENECHEA, G.R. and RANKIN, R.:

Fully computable error estimation of a nonlinear, positivity-preserving, discretization of the convection-diffusion-reaction equation.

SIAM J. Scientific Computing, 30(5), A1903–A1927, (2017).

 

37. BARRENECHEA, G.R. and KNOBLOCH, P.:

An analysis of the group finite element formulation.

Applied Numerical Mathematics, 118, 238–248, (2017).

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36. BARRENECHEA, G.R., JOHN, V., and KNOBLOCH, P.:

An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes.

Mathematical Methods and Models in Applied Sciences (M3AS), 27(3), 525–548, (2017).

 

35. BARRENECHEA, G.R., BOULTON, L. and BOUSSAID, N.:

Local two-sided bounds for eigenvalues of self-adjoint operators.

Numerische Mathematik, 135, 953–986, (2017).

 

34. BARRENECHEA, G.R., BURMAN, E., and KARAKATSANI, F.:

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, 1169–1193, (2017).

 

33. BARRENECHEA, G.R., BURMAN, E., and KARAKATSANI, F.:

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

Numerische Mathematik, 135, 521–545, (2017).

 

32. BARRENECHEA, G.R., JOHN, V., and KNOBLOCH, P.:

Analysis of algebraic flux correction schemes.

SIAM Journal on Numerical Analysis, 54(4), 2427–2451, (2016).

 

31. BARRENECHEA, G.R., BARRIOS, T. and WACHTEL, A.:

Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model.

Calcolo, 52, 343–369, (2015).

 

30. BARRENECHEA, G.R., JOHN, V., and KNOBLOCH, P.:

Some analytical results for an algebraic flux correction scheme for a steady convection–diffusion equation in 1D.

IMA Journal of Numerical Analysis, 35, 1729–1756, (2015).

 

29. AINSWORTH, M., BARRENECHEA, G.R., and WACHTEL, A.:

Stabilization of high aspect ratio mixed finite elements for incompressible flow.

SIAM Journal on Numerical Analysis, 53(2), 1107–1120, (2015).

 

28. BARRENECHEA, G.R., BOULTON, L. and BOUSSAID, N.:

Finite element eigenvalue enclosures for the Maxwell operator.

SIAM Journal on Scientific Computing, 36(6), A2887-A2906, (2014).

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27. AINSWORTH, M., ALLENDES, A., BARRENECHEA, G.R. and RANKIN, R.:

Fully computable a posteriori error bounds for stabilized FEM approximations of convection- reaction-diffusion problems in three dimensions.

International Journal for Numerical Methods in Fluids, 73(9), 765–790, (2013).

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26. BARRENECHEA, G.R., JOHN, V., and KNOBLOCH, P.:

A local projection stabilized finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations.

ESAIM M2AN, 47 (5), 1335 –1366, (2013).

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25. AINSWORTH, M., ALLENDES, A., BARRENECHEA, G.R., and RANKIN, R.:

On the adaptive selection of the parameter in stabilized finite element approximations.

SIAM Journal on Numerical Analysis, 51(3), 1585–1609, (2013).

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24. BARRENECHEA, G.R. and CHOULY, F.:

A local projection stabilized method for fictitious domains.

Applied Mathematics Letters, 25, 2071-2076, (2012).

 

23. AINSWORTH, M., ALLENDES, A., BARRENECHEA, G.R., and RANKIN, R.:

Computable error bounds for nonconforming Fortin-Soulie finite element approximation of the Stokes problem.

IMA Journal of Numerical Analysis,32(2), 417-447, (2012).

 

22. ARAYA, R., BARRENECHEA, G.R., POZA, A. and VALENTIN, F.:

Convergence analysis of a residual local projection method for the Navier-Stokes equation.

SIAM Journal on Numerical Analysis, 50(2), 669-699, (2012).

 

21. ARAYA, R., BARRENECHEA, G.R., JAILLET, F. and RODRIGUEZ, R.:

Finite-element analysis of a static fluid-solid interaction problem.

IMA Journal of Numerical Analysis, 31(3), 886-913, (2011).

 

20. BARRENECHEA, G.R. and VALENTIN, F.:

Beyond pressure stabilization: a low order local projection method for the Oseen equation.

International Journal for Numerical Methods in Engineering, 86 (7), 801-815, (2011).

 

19. ALLENDES, A., BARRENECHEA, G.R., HERNANDEZ, E. and VALENTIN, F.:

A two-level enriched finite element method for a mixed problem.

Mathematics of Computation, 80 (273), 11-41, (2011).

 

18. BARRENECHEA, G.R. and VALENTIN, F.:

Consistent local projection stabilized  finite element methods.

SIAM Journal on Numerical Analysis, 48 (5), 1801-1825, (2010).

 

17. BARRENECHEA, G.R. and VALENTIN, F.:

A residual local projection method for the Oseen Equation.

Computer Methods in Applied Mechanics and Engineering, 199 (29-32),1906-1921, (2010).

 

16. BARRENECHEA, G.R., FRANCA, L.P. and VALENTIN, F.:

A symmetric nodal locally conservative finite element method for the Darcy equation.

SIAM Journal on Numerical Analysis, 47 (5), 3652-3677, (2009).

 

15. ARAYA, R., BARRENECHEA, G.R., FRANCA, L.P. and VALENTIN, F.:

Stabilization arising from PGEM: a review and further developments.

Applied Numerical Mathematics, 59(9), 2065-2081, (2009).

 

14. BARRENECHEA, G.R. and CHOULY, F.:

A finite element method for the resolution of the Reduced Navier-Stokes/Prandtl equations.

ZAMM, 89(1), 54-68, (2009).

 

13. ARAYA, R., BARRENECHEA, G.R. and POZA, A.:

An adaptive stabilized finite element method for the generalized Stokes problem.

Journal of Computational and Applied Mathematics, 214, 457-479, (2008).

 

12. BARRENECHEA, G.R., and BLASCO, J.:

Pressure stabilization of finite element approximations of time dependent incompressible flow problems.

Computer Methods in Applied Mechanics and Engineering, 197(1-4), 219-231, (2007).

 

11. BARRENECHEA, G.R., FRANCA, L.P. and VALENTIN, F.:

A Petrov-Galerkin enriched method: A mass conservative finite element method for the Darcy equation.

Computer Methods in Applied Mechanics and Engineering, 196, 21-24, 2449-2464, (2007).

 

10. ARAYA, R., BARRENECHEA, G.R. and VALENTIN, F.:

A Stabilized finite element method for the Stokes problem including element and edge residuals.

IMA Journal of Numerical Analysis, 27, 192-197, (2007).

 

9. ARAYA, R., BARRENECHEA, G.R. and VALENTIN, F.:

Stabilized finite element methods based on multiscale enrichment for the Stokes problem.

SIAM Journal on Numerical Analysis, 44,1, 322-348, (2006).

 

8. BARRENECHEA, G.R. and VALENTIN, F.:

Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem.

Comptes Rendus de l’Académie des Sciences de Paris Serie I Math., 341, 10, 635-640,(2005).

 

7. BARRENECHEA, G. and VALENTIN, F. :

An unusual stabilized finite element method for a generalized Stokes problem.

Numerische Mathematik, 92, 4, pp. 653{677, (2002).

 

6. BARRENECHEA, G.R., LE TALLEC, P. and VALENTIN, F.:

New wall laws for the unsteady incompressible Navier-Stokes equations on rough domains.

M2AN, 36, 2, pp.177-203, (2002).

 

5. BARRENECHEA, G.R. and GATICA, G.N.:

A primal mixed formulation for exterior transmission problems in R2.

Numerische Mathematik, 88, 2, pp. 237-253, (2001).

 

4. BARRENECHEA, G.R., GATICA, G.N. and HSIAO, G.C.:

Weak solvability of interior transmission problems via mixed finite elements and Dirichlet-to-Neumann mappings.

Journal of Computational and Applied Mathematics, 100, 2, pp. 145-160, (1998).

 

3. BARRENECHEA, G.R., BARRIENTOS, M.A. and GATICA, G.N.:

On the numerical analysis of finite element and Dirichlet-to-Neumann methods for nonlinear exterior transmission problems.

Numerical Functional Analysis and Optimization, 19, 7-8, pp. 705-735, (1998).

 

2. BARRENECHEA, G.R., GATICA, G.N. and THOMAS, J.-M.:

Primal mixed formulations for the coupling of FEM and BEM. Part I: Linear problems.

Numerical Functional Analysis and Optimization, 19, 1-2, pp. 7-32, (1998).

 

1. BARRENECHEA, G.R. and GATICA, G.N.:

On the coupling of boundary integral and finite element methods with nonlinear transmission conditions.

Applicable Analysis, 62, 1-2, pp. 181-210, (1996).

 

Articles in proceedings of symposia and conferences:

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11. BARRENECHEA, G.R., BOSY, M., DOLEAN, V.:

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions.

ICOSAHOM Proceedings, to appear.

10. PASCARELLA, G., BARRENECHEA, G.R., and FOSSATI, M.:

Reconstruction and Physical Insight of Complex Unsteady Flows through Reduced Order Modeling.

7th European Conference on Computational Fluid Dynamics, Glasgow June 2018.

9. BARRENECHEA, G.R. and WACHTEL, A.:

A note on the stabilised Q1/P0 method on quadrilaterals with high aspect ratios.

Proceedings of BAIL, 2014. Springer Verlag, page 1-10, 2016.

8. BARRENECHEA, G.R., JOHN, V. and KNOBLOCH, P.:

A nonlinear local projection stabilization for convection-diusion-reaction equations,

in A. Cangiani, R. Davidchack, E. H. Georgoulis, A. Gorban, J. Levesley, M. Tretyakov (eds.), ENUMATH '11 Proceedings, Leicester, Springer, 2012.

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7. ARAYA, R., BARRENECHEA, G.R., POZA. A. and VALENTIN, F.:

On a Residual Local Projection Method for the Incompressible Navier- Stokes Equations.

XXXI CILAMCE, Vol XXIX, p.p 4563-4572, Buenos Aires, Argentina, 2010.

 

6. BARRENECHEA, G.R. and VALENTIN, F.:

A new local projection stabilized finite element method.

Proceedings of XXI Congreso de Ecuaciones Diferenciales y Aplicaciones, CEDYA 2009, Ciudad Real, Spain, 2009. ISBN:978-84-692-6473-7.

 

5. ARAYA, R., BARRENECHEA, G.R., GALDAMES, F.J., JAILLET, F. and RODRIGUEZ, R.:

Adaptive mesh and finite element analysis of coupled fluid/structure: application to brain deformations.

Proceedings of SURGETICA'2007, Chambry (F), Sept. 2007, pp 117-121, ISBN 978-2-84023-526-2

 

4. ARAYA, R., BARRENECHEA, G.R. and VALENTIN, F.:

Stabilizing the P1-P0 element for the Stokes problem via multiscale enrichment.

Proceedings of ENUMATH 2005, A. Bermudez et. al. (Eds), Springer-Verlag, pp. 783-790.

 

3. ARAYA, R., BARRENECHEA, G.R. and POZA, A.:

A posteriori error analysis and an adaptive strategy for a generalized Stokes problem.

In Mecanica Computacional, vol. XXIV, Axel Larreteguy, Ed., pp. 1211-1227, Proceedings of MECOM 2005, Buenos Aires, Argentina. November 2005.

 

2. BARRENECHEA, G.R., FERNANDEZ, M.A. and VIDAL, C.I.:

A stabilized finite element method for generalized incompressible flow problems.

In Mecanica Computacional, vol. XXIII, G. Buscaglia, E. Dari, O. Zamonsky (Eds.), Proceedings of ENIEF 2004, Bariloche, Argentina. November 2004.

 

1. BARRENECHEA, G.R. and FERNANDEZ, M.A.:

A stabilized finite element method for the linearized Navier-Stokes equation with dominating reaction.

ECCOMAS 2004. Proceedings of the European Congress on Computational Methods in Applied Science and Engineering. P. Neittaanmaki et al., eds., CD-ROM, 2004.