Cursos que dicta

Pregrado

• Cálculo III.
• Cálculo Numérico.

Postgrado

• Teoría de Operadores Lineales.
• Aspectos Computacionales del Método de Elementos Finitos.
• Tópicos de Análisis de Error A-posteriori.

Producción Científica

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

• 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, 2, 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).
• 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).
• Sergio Caucao, Marco Discacciati, Gabriel N. Gatica, Ricardo 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, Gabriel N. Gatica, Ricardo 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).
• Sergio Caucao, Gabriel N. Gatica, Ricardo 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).
• Sergio Caucao, Gabriel N. Gatica, Ricardo Oyarzúa, Ivana 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).
• Sergio Caucao, Gabriel N. Gatica, Ricardo 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).
• Sergio Caucao, David Mora, Ricardo 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).

Líneas de Investigación