Aspectos Computacionales del Método de Elementos Finitos
Tópicos de Análisis de Error A-Posteriori
Área de Investigación
Análisis Numérico de Ecuaciones Diferenciales Parciales
Método de Elementos Finitos Mixtos
Análisis de Error A-Posteriori
Proyectos
(Investigador Responsable). 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).
(Investigador Responsable). Proyecto FONDECYT No. 11220393. Concurso de Proyectos Fondecyt de Iniciación en Investigación 2022: Finite Element Methods for Brinkman-Forchheimer and Related Problems. (Marzo 2022 – Marzo 2025).
(Investigador Asociado). Proyecto Basal FB210005 CMM-UChile. Concurso Programa de Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia 2021, ANID-Chile. (Noviembre 2021 – Noviembre 2031).
(Investigador Responsable). Programa PAI de Conicyt, Proyecto No. 77190084. Convocatoria Nacional Subvención a la Instalación en la Academia 2019: “Métodos de Elementos Finitos para Modelos de Interacción Fluido-Estructura Poroelástica y Problemas Afines”. (Enero 2020 – Diciembre 2022).
Publicaciones
S. Caucao, G.N. Gatica, S.R. Medrado, and Y.D. Sobral: Nonlinear twofold saddle point-based mixed finite element methods for a regularized mu(I)-rheology model of granular materials. Journal of Computational Physics, vol. 520, Paper No. 113462, (2025).
S. Caucao, G.N. Gatica, and J.P. Ortega: A three-field mixed finite element method for the convective Brinkman-Forchheimer problem with varying porosity. Journal of Computational and Applied Mathematics, vol 451, Art. Num. 116090, (2024).
S. Caucao, T. Li, and I. Yotov: An augmented fully-mixed formulation for the quasistatic Navier-Stokes-Biot model. IMA Journal of Numerical Analysis, vol. 44, 2, pp. 1153-1210, (2024).
S. Caucao and J. Esparza: An augmented mixed FEM for the convective Brinkman-Forchheimer problem: a priori and a posteriori error analysis. Journal of Computational and Applied Mathematics, vol 438, Art. Num. 115517, (2024).
S. Carrasco, S. Caucao, and G.N. Gatica: New mixed finite element methods for the coupled convective Brinkman-Forchheimer and double-diffusion equations. Journal of Scientific Computing, vol. 97, 3, article: 61, (2023).
S. Caucao, G.N. Gatica, and L.F. Gatica: A Banach spaces-based mixed finite element method for the stationary convective Brinkman-Forchheimer problem. Calcolo, vol. 60, 4, article: 51, (2023).
S. Caucao, E. Colmenares, G.N. Gatica, and C. Inzunza: A Banach spaces-based fully-mixed finite element method for the stationary chemotaxis-Navier-Stokes problem. Computer and Mathematics with Applications, vol. 145, pp. 65-89, (2023).
L. Angelo, J. Camaño, and S. Caucao: A five-field mixed formulation for stationary magnetohydrodynamic flows in porous media. Computer Methods in Applied Mechanics and Engineering, vol. 414, Art. Num. 116158, (2023).
S. Caucao and M. Discacciati: A mixed FEM for the coupled Brinkman-Forchheimer/Darcy problem. Applied Numerical Mathematics, vol. 190, pp. 138-154, (2023).
S. Caucao, G.N. Gatica, and J.P. Ortega: A posteriori error analysis of a Banach spaces-based fully mixed FEM for double-diffusive convection in a fluid-saturated porous medium. Computational Geosciences, vol. 27, 2, pp. 289-316, (2023).
V. Anaya, R. Caraballo, S. Caucao, L.F. Gatica, R. Ruiz-Baier, and I. Yotov: “A vorticity-based mixed formulation for the unsteady Brinkman-Forchheimer equations”. Computer Methods in Applied Mechanics and Engineering, vol. 404, Art. Num. 115829, (2023).
S. Caucao, R. Oyarzúa, and S. Villa-Fuentes: “A posteriori error analysis of a momentum and thermal energy conservative mixed FEM for the Boussinesq equations”. Calcolo, vol. 59, 4, article: 45, (2022).
S. Caucao, G.N. Gatica, R. Oyarzúa, and P. Zúñiga: “A posteriori error analysis of a mixed finite element method for the coupled Brinkman-Forchheimer and double-diffusion equations”. Journal of Scientific Computing, vol 93, article:50, (2022).
S. Caucao, T. Li, and I. Yotov: “A multipoint stress-flux mixed finite element method for the Stokes-Biot model”. Numerische Mathematik, vol. 152, pp. 411-473, (2022).
S. Caucao, R. Oyarzúa, S. Villa-Fuentes, and I. Yotov: “A three-field Banach spaces-based mixed formulation for the unsteady Brinkman-Forchheimer equations”. Computer Methods in Applied Mechanics and Engineering, vol. 394, Art. Num. 114895, (2022).
S. Caucao, G.A. Benavides, G.N. Gatica, and A.A. Hopper: “A new non-augmented and momentum-conserving fully-mixed finite element method for a coupled flow-transport problem”. Calcolo, vol. 59, 1, article: 6, (2022).
J. Camaño, S. Caucao, R. Oyarzúa, and S. Villa-Fuentes: “A posteriori error analysis of a momentum conservative Banach spaces based mixed-FEM for the Navier-Stokes problem”. Applied Numerical Mathematics, vol. 176, pp. 134-158, (2022).
G.A. Benavides, S. Caucao, G.N. Gatica, and A.A. Hopper: “A new non-augmented and momentum-conserving fully-mixed finite element method for a coupled flow-transport problem”. Calcolo, vol. 59, 1, article: 6, (2022).
S. Caucao, G.N. Gatica, and J.P. Ortega: “A fully-mixed formulation in Banach spaces for the coupling of the steady Brinkman-Forchheimer and double-diffusion equations”. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, 6, pp. 2725-2758, (2021).
S. Caucao and I. Yotov: “A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations”. IMA Journal of Numerical Analysis, vol. 41, 4, pp. 2708-2743, (2021).
S. Caucao, G.N. Gatica, R. Oyarzúa, F. Sandoval: “Residual-based a posteriori error analysis for the coupling of the Navier-Stokes and Darcy-Forchheimer equations“. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 55, 2, pp. 659-687, (2021).
S. Caucao, G.N. Gatica, F. Sandoval: “A fully-mixed finite element method for the coupling of the Navier-Stokes and Darcy-Forchheimer equations”. Numerical Methods for Partial Differential Equations, vol. 37, 3, pp. 2550-2587, (2021).
S. Caucao, G.N. Gatica, R. Oyarzúa, and N. Sánchez: “A fully-mixed formulation for the steady double-diffusive convection system based upon Brinkman-Forchheimer equations”. Journal of Scientific Computing, vol. 85, 2, article:44, (2020).
S. Caucao, R. Oyarzúa, and S. Villa-Fuentes: “A new mixed-FEM for steady-state natural convection models allowing conservation of momentum and thermal energy”. Calcolo, vol. 57, article:36, (2020).
G.A. Benavides, S. Caucao, G.N. Gatica, and A.A. Hopper: “A Banach spaces-based analysis of a new mixed-primal finite element method for a coupled flow-transport problem“. Computer Methods in Applied Mechanics and Engineering, vol. 371, Art. Num. 113285, (2020).
S. Caucao, M. Discacciati, G.N. Gatica, and R. Oyarzúa: “A conforming mixed finite element method for the Navier-Stokes/Darcy-Forchheimer coupled problem”. ESAIM Mathematical Modelling and Numerical Analysis, vol. 54, 5, pp. 1689-1723, (2020).
S. Caucao, G.N. Gatica, and R. Oyarzúa: “A posteriori error analysis of an augmented fully mixed formulation for the nonisothermal Oldroyd-Stokes problem”. Numerical Methods for Partial Differential Equations, vol. 35, 1, pp. 295-324, (2019).
S. Caucao, G.N. Gatica, and R. Oyarzúa: “Analysis of an augmented fully-mixed formulation for the coupling of the Stokes and heat equations”. ESAIM Mathematical Modelling and Numerical Analysis, vol. 52, 5, pp. 1947-1980, (2018).
S. Caucao, G.N. Gatica, R. Oyarzúa, and I. Šebestová: “A fully-mixed finite element method for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity”. Journal of Numerical Mathematics, vol. 25, 2, pp. 55-88, (2017).
S. Caucao, G.N. Gatica, and R. Oyarzúa: “A posteriori error analysis of a fully-mixed formulation for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity”. Computer Methods in Applied Mechanics and Engineering, vol. 315, pp. 943-971, (2017).
S. Caucao, D. Mora, and R. Oyarzúa: “A priori and a posteriori error analysis of a pseudostress-based mixed formulation of the Stokes problem with varying density”. IMA Journal of Numerical Analysis, vol. 36, 2, pp. 947-983, (2016).
