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 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 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. 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).
Verónica Anaya, Ruben Caraballo, Sergio Caucao, Luis F. Gatica, Ricardo Ruiz-Baier, Ivan 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).
Sergio Caucao, Ricardo Oyarzúa, Segundo 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).
Sergio Caucao, Gabriel N. Gatica, Ricardo Oyarzúa, Paulo 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).
Sergio Caucao, Tongtong Li, Ivan Yotov. “A multipoint stress-flux mixed finite element method for the Stokes-Biot model”. Numerische Mathematik, vol. 152, pp. 411-473, (2022).
Sergio Caucao, Ricardo Oyarzúa, Segundo Villa-Fuentes, Ivan 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).
Sergio Caucao, Gonzalo A. Benavides, Gabriel N. Gatica, Alejandro 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).
Jessika Camaño, Sergio Caucao, Ricardo Oyarzúa, Segundo 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).
Gonzalo A. Benavides, Sergio Caucao, Gabriel N. Gatica, Alejandro 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).
Sergio Caucao, Gabriel N. Gatica, Juan 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).
Sergio Caucao, Ivan Yotov, “A Banach space mixed formulation for the unsteady Brinkman-Forchheimer equations”. IMA Journal of Numerical Analysis, vol. 41, 4, pp. 2708-2743, (2021).
Sergio Caucao, Gabriel N. Gatica, Ricardo Oyarzúa, Felipe 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).
Sergio Caucao, Gabriel N. Gatica, Felipe 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).
Sergio Caucao, Gabriel N. Gatica, Ricardo Oyarzúa, Nestor 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).
Sergio Caucao, Ricardo Oyarzúa, Segundo 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).
Gonzalo A. Benavides, Sergio Caucao, Gabriel N. Gatica, Alejandro 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, 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, 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, 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, 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, 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, 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).
