Departamento

Matemáticas y Física Aplicadas.

Cursos que dicta

Pregrado

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

Postgrado

Análisis Funcional, Teoría de Elementos Finitos,  Métodos de Elementos Finitos Mixtos, Metodos de Galerkin discontinuos,  Tópicos de Análisis de Error a Posteriori.

Proyectos

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

  • Tomás Barrios, Rommel 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).
  • Tomás Barrios, José Manuel Cascón, María 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.
  • Tomás Barrios, Edwin Behrens, Rommel 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).
  • Tomás Barrios, José Manuel Cascón, María González: Adaptive augmented mixed FEM for the Oseen problem with mixed boundary conditions. Monografías Matemáticas García de Galdeano, vol 42, pp. 25-34, University of Zaragoza Press, Spain.(2019).
  • Tomás Barrios, Edwin Behrens, María 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).
  • Tomás Barrios, Rommel Bustinza, Galina C. García, María 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).
  • Tomás Barrios, Edwin Behrens, María 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).
  • Tomás P. Barrios, Rommel Bustinza, 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).
  • Tomás P. Barrios, José M. Cascón, María 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).
  • Tomás P. Barrios, Rommel Bustinza, Víctor 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).
  • Tomás P. Barrios, Edwin Behrens, Rommel Bustinza. “A note on a priori error estimates for augmented mixed methods”. Applied Mathematics Letters, vol. 57, pp. 139-144, (2016).
  • Tomás Barrios, José Manuel Cascón, María 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. (2015).
  • Gabriel Barrenechea, Tomás Barrios, Andreas Wachtel. “Stabilized finite element methods for a bending moment formulation of the Reissner-Mindlin plate model”. Calcolo, vol. 52, pp. 343-369, (2015).
  • Tomás Barrios, José Manuel Cascón, María 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).
  • Tomás Barrios, Edwin Behrens, María 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.
  • Tomás Barrios, Rommel Bustinza, Galina C. García, María 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.
  • Tomás P. Barrios, Edwin Behrens, María González. “Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity”. Applied Numerical Mathematics, vol. 84, pp. 46-65, (2014).
  • Tomás Barrios, José Manuel Cascón, María 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. (2014).
  • T. Barrios, 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).
  • T. Barrios, R. Bustinza, G. García, 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).
  • T. Barrios, E. M. Behrens, 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).
  • Barrios T., Bustinza R. 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).
  • Tomás Barrios, Rommel 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).
  • Barrios, T., Bustinza, R. An augmented discontinuous Galerkin method for elliptic problems”. Comptes Rendus de l’Académie des Sciences Serie I: Mathématique, 344, 53-58, (2007).
  • Barrios, T., Gatica, G.N. 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).
  • Barrios, T., Gatica, G.N.,  Paiva, F. “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).
  • Tomás Barrios, Rommel Bustinza. “An augmented LDG method for linear diffusion problems”. PAMM- Proceedings in Applied Mathematics and Mechanics. 7, pp. 220057-220058. (2007).
  • Barrios T., Gatica G.N., Paiva F. “A wavelet-based stabilization of the mixed finite element method with Lagrange multipliers”. Applied Mathematics Letters, vol. 19, 3, pp. 244-250, (2006).
  •  Barrios T., Gatica G.N., González M., Heuer N. “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).
  • Barrios T. “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).
  • Barrios T., Gatica G.N., Gatica L.F. ” 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).
  • Rodolfo Araya, Tomás Barrios, Gabriel N. Gatica, Norbert 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).

Líneas de investigación

Análisis Numérico.