Tomás Barrios Faúndez

  • Cargo: Profesor Asociado/Director DMFA
  • Título académico: Ingeniero Matemático
  • Grado académico: Doctor en Ciencias Aplicadas con mención en Ingeniería Matemática, Universidad de Concepción, 2006
  • Dependencia de trabajo: Oficina Nº 5, DMFA
  • Correo electrónico: tomas@ucsc.cl
  • Teléfono: +56 - 41 - 2345684

Enlaces de Interés

Cursos que Imparte

Pregrado

  • Cálculo I, Cálculo II, Cálculo III, Cálculo Complejo
  • Ecuaciones Diferenciales
  • Cálculo Numérico

Postgrado

  • Análisis Funcional
  • Teoría de Elementos Finitos
  • Métodos de Elementos Finitos Mixtos
  • Métodos de Galerkin Discontinuos
  • Tópicos de Análisis de Error A-Posteriori

Área de Investigación

  • Análisis Numérico

Proyectos

  • (Investigador Asociado). Proyecto DI-UCSC FGII 06/2024. Fondo Interno para Fortalecer los Grupos de Investigación e Innovación 2024: Grupo de Investigación en Análisis Numérico y Cálculo Científico (GIANuC²). (Octubre 2024 – Octubre 2025).
  • (Investigador Asociado). Proyecto DI-UCSC No. FGII 04/2023. Fondo Interno para Fortalecer los Grupos de Investigación e Innovación 2023:
    Grupo de Investigación en Análisis Numérico y Cálculo Científico (GIANuC²). (October 2023 – October 2024).
  • 2020 – 2024: “Error Estimates for new Computer Methods in Continuum Mechanic”. FONDECYT 1200051,  Investigador Principal.
  • 2016- 2020: “Circumventing the inf-sup condition via stabilisation techniques: A priori and a posteriori error analyses”.  FONDECYT 1160578, Investigador Principal.
  • 2014: “Desarrollo de técnicas numéricas para la identificación de parámetros constitutivos en medios porosos”. PROYECTO AL14-PID-07 (Universidad Politécnica de Madrid, España), Co-investigador.
  • 2013 – 2017: “Further applications of stabilized DG and HDG methods to linear and nonlinear steady problems in continuum mechanics”. FONDECYT 1130158, Co-investigador.
  • 2008 – 2012: “New developments of augmented discontinuous Galerkin methods for boundary value problems in continuum mechanics”. FONDECYT 1080168, Co-investigador.
  • 2006 – 2008: “A priori and a posteriori error analyses of the stabilized mixed finite element method in elasticity and fluid mechanics”. FONDECYT 11060014, Investigador Principal.

Publicaciones

[ 36 ]

T.P. Barrios and R. Bustinza: An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem. Numerical Methods for Partial Differential Equations, vol. 40, 5, e23100, (2024).

[ 35 ]

T.P. Barrios, R. Bustinza, and C. Campos: A note on a posteriori error estimates for dual mixed methods with mixed boundary condition. Numerical Methods for Partial Differential Equations, vol. 39, 5, pp. 3897-3918, (2023).

[ 34 ]

T.P. Barrios, E. Behrens, and R. Bustinza: Numerical Analysis of a stabilized scheme applied to incompressible elasticity problems with Dirichlet and with mixed boundary conditions. Advances in Computational Mathematics, vol. 48, issue 4, Article Number 43. (2022).

[ 33 ]

T.P. Barrios, R. Bustinza, and C. Campos: An a posteriori error estimator for a non homogeneous Dirichlet problem considering a dual mixed formulation. Trends in Computational and Applied Mathematics, vol.23, Issue 3, pp. 549-568. (2022).

[ 32 ]

T.P. Barrios, E. Behrens, and R. Bustinza: An a posteriori error estimate for a dual mixed method applied to Stokes system with non null source terms. Advances in Computational Mathematics, vol. 47, issue 5, Article Number 77. (2021).

[ 31 ]

T.P. Barrios and R. Bustinza: An a-priori error analysis for discontinuous Lagrangian finite elements applied to nonconforming dual-mixed formulations: Poisson and Stokes problems. Electronic Transactions on Numerical Analysis (ETNA), vol. 52, pp. 455-479, (2020).

[ 30 ]

T.P. Barrios, J.M. Cascón, and M. González: On an adaptive stabilized mixed finite element method for the Oseen problem with mixed boundary conditions. Computer Methods in Applied Mechanics and Engineering, vol. 365, (2020), 113007.

[ 29 ]

T.P. Barrios, E. Behrens, and R. Bustinza: A stabilised mixed method applied to Stokes system with non homogeneous source terms: The stationary case. International Journal for Numerical Methods in Fluids, vol. 92, Issue 6, pp. 509-527, (2020).

[ 28 ]

T.P. Barrios, E. Behrens, and M. González: A posteriori error analysis of an augmented dual-mixed method in linear elasticity with mixed boundary conditions. International Journal of Numerical Analysis and Modeling, vol 16 (5), pp. 804-824. (2019).

[ 27 ]

T.P. Barrios, R. Bustinza, G.C. García, and M. González: A posteriori error analysis of a velocity-pseudostress formulation of the generalized Stokes problem. Journal of Computational and Applied Mathematics, vol. 357, pp. 349-365, (2019).

[ 26 ]

T.P. Barrios, E. Behrens, and M. González: New a-posteriori error estimator for an stabilised mixed method applied to incompressible fluid flows. Applied Mathematics and Computation, Vol. 351, pp. 37-47, (2019).

[ 25 ]

T.P. Barrios, R. Bustinza, and Felipe Sánchez: Analysis of DG aproximations for the Stokes problem based on velocity-pseudostress formulation. Numerical Methods for Partial Differential Equations, vol. 33, 5, pp. 1540-1564, (2017).

[ 24 ]

T.P. Barrios, J.M. Cascón, and M. González: Augmented mixed finite element method for the Oseen problem: A priori and a posteriori error analysis. Computer Methods in Applied Mechanics and Engineering, vol. 313, pp. 216-238, (2017).

[ 23 ]

T.P. Barrios, R. Bustinza, and V. Dominguez: Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frecuency regime. Journal of Computational and Applied Mathematics, vol. 300, pp. 312–340, (2016).

[ 22 ]

T.P. Barrios, E. Behrens, and R. Bustinza: A note on a priori error estimates for augmented mixed methods. Applied Mathematics Letters, vol. 57, pp. 139-144, (2016).

[ 21 ]

T.P. Barrios, J.M. Cascón, and M. González: A posteriori error estimation of a stabilized mixed finite element method for Darcy flow. In Book: Boundary and Interior Layers – Computational & Asymptotic Methods, BAIL 2014 (Edited by Petr Knobloch). Springer series Lecture Notes in Computational Science and Engineering, Vol 108, pp 13 – 23.

[ 20 ]

G. Barrenechea, T.P. Barrios, and A. Wachtel: Stabilized finite element methods for a bending moment formulation of the Reissner-Mindlin plate model. Calcolo, vol. 52, pp. 343-369, (2015).

[ 19 ]

T.P. Barrios, J.M. Cascón, and M. Gonzaléz: A posteriori error analysis of a stabilized mixed finite element method for Darcy flow. Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 909-922, (2015).

[ 18 ]

T.P. Barrios, E. Behrens, and M. González: New a posteriori error estimator for an augmented mixed FEM in linear elasticity. Numerical Mathematics and Advanced Applications – ENUMATH 2013, ( Edited by A. Addulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso), Lecture Notes in Computational Science and Engineering, Vol 103, pp. 263-271, Springer International Publishing Switzerland, 2015.

[ 17 ]

T.P. Barrios, R. Bustinza, G.C. García, and M. González: An a posteriori error estimator  for a new stabilized formulation of the Brinkman problem. Numerical Mathematics and Advanced Applications – ENUMATH 2013, ( Edited by A. Addulle, S. Deparis, D. Kressner, F. Nobile, M. Picasso), Lecture Notes in Computational Science and Engineering, Vol 103, pp. 253-261, Springer International Publishing Switzerland, 2015.

[ 16 ]

T.P. Barrios, E. Behrens, and M. González: Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity. Applied Numerical Mathematics, vol. 84, pp. 46-65, (2014).

[ 15 ]

T.P. Barrios, J.M. Cascón, and M. González: Adaptive solutions of a stabilized mixed finite element method for porous media equations. Mecánica Computacional, Vol XXXIII, Nº 30, G. Bertolino, M. Cantero, M. Storti and F. Teruel (Editors), pp. 1909 – 1917, AMCA, Argentina. ISSN 1666-6070.

[ 14 ]

T.P. Barrios and R. Bustinza: An a-posteriori error analysis of an augmented discontinuous Galerkin formulation for Darcy flow. Numerische Mathematik, vol. 120, 2, pp. 231-269. (2012).

[ 13 ]

T.P. Barrios, R. Bustinza, G. García, and H. Hernández: On stabilized mixed methods for generalized Stokes problem based on the velocity-pseudostress formulation: A priori error estimates. Computer Methods in Applied Mechanics and Engineering, vol. 237-240, pp. 78-87, (2012).

[ 12 ]

T.P. Barrios, E. M. Behrens, and M. González: A posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions. Computer Methods in Applied Mechanics and Engineering, vol. 200, 3-4, pp. 101-113, (2011).

[ 11 ]

T.P. Barrios and R. Bustinza: A-priori and a-posteriori error analysis of an augmented Galerkin discontinuous formulation. IMA Journal of Numerical Analysis, vol. 30, 4, pp. 987-1008, (2010).

[ 10 ]

T.P. Barrios and R. Bustinza: An augmented DG scheme for porous media equations. In book: Numerical Mathematics and Advanced Applications, Proceeding ENUMATH 2007, K. Kunish, G. Of and O. Steinbach (eds.), pp. 315-322. Springer Verlag. (2008).

[ 9 ]

T.P. Barrios and R. Bustinza: An augmented discontinuous Galerkin method for elliptic problems. Comptes Rendus de l’Académie des Sciences Serie I: Mathématique, 344, 53-58, (2007).

[ 8 ]

T.P. Barrios and G.N. Gatica: An augmented mixed finite element method with Lagrange multipliers: a-priori and a-posteriori error analyses. Journal of Computational and Applied Mathematics, 200, 653-676, (2007).

[ 7 ]

T.P. Barrios, G.N. Gatica, and F. Paiva: A-priori and a-posteriori error analysis of a wavelet-based stabilization of the mixed finite element method. Numerical Functional Analysis and Optimization, 28, 265-286, (2007).

[ 6 ]

T.P. Barrios and R. Bustinza: An augmented LDG method for linear diffusion problems. PAMM- Proceedings in Applied Mathematics and Mechanics. 7, pp. 220057-220058. (2007).

[ 5 ]

T.P. Barrios, G.N. Gatica, and F. Paiva: A wavelet-based stabilization of the mixed finite element method with Lagrange multipliers. Applied Mathematics Letters, vol. 19, 3, pp. 244-250, (2006).

[ 4 ]

T.P. Barrios, G.N. Gatica, M. González, and N. Heuer: A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 40, 5, pp. 843-869, (2006).

DOI

[ 3 ]

T.P. Barrios: Adaptive solutions of an augmented mixed finite mixed finite element scheme for linear elasticity. SCIENTA, Series A: Mathematical Sciences, vol. 13, pp. 46-56, (2006).

DOI

[ 2 ]

T.P. Barrios, G.N. Gatica, and L.F. Gatica: On the numerical analysis of a nonlinear elliptic problem via mixed-FEM and Lagrange multipliers. Applied Numerical Mathematics, vol. 48, 2, pp. 135-155, (2004).

 DOI

[ 1 ]

R. Araya, T.P. Barrios, G.N. Gatica, and N. Heuer: A-posteriori error estimates for a mixed-FEM formulation of a non-linear elliptic problem. Computer Methods in Applied Mechanics and Engineering, vol. 191, 21-22, pp. 2317-2336. (2002).

DOI