Numerical methods for partial differential equations; Finite element methods; Adaptivity in finite element methods; Finite element methods for Optimal Control Problems

- Gilberto Campaña, Ph.D. in Mathematics. 2020-Present - In progress
Advisors: Alejandro Allendes and Enrique Otárola. UTFSM
Title: Finite element methods for PDEs under singular forcing data.

- Gustavo García, Computer Engineering. 2019 - (100/100)
Advisor: Alejandro Allendes. UTFSM
Title: Stabilized finite element algorithms for linear and non-linear fluid flow problems.

- Francisco Fuica, Ph.D. in Mathematics. 2018-Present - In progress
Advisors: Alejandro Allendes and Enrique Otárola. UTFSM
Title: Adaptive finite element methods in linear and nonlinear PDE–constrained optimization.

- Daniel Quero, Master of Science. 2018-Present - In progress
Advisors: Alejandro Allendes and Enrique Otárola. UTFSM
Title: A posteriori error estimation for finite element approximations of a PDE–constrained optimization problem in fluid dynamics involving Dirac measures.

- Francisco Fuica, Master of Science. 2017 (100/100)
Advisors: Alejandro Allendes and Enrique Otárola. UTFSM
Title: Adaptive finite element methods in sparse PDE–constrained optimization.

- Kevin Andrews, Industrial Engineering. 2017
Advisors: Alejandro Allendes and Gilberto Campaña. UTFSM
Title: Adaptive finite elements for pollution transport.

- Daniel Quero, Mathematical Engineering. 2017
Advisors: Alejandro Allendes and Enrique Otárola. UTFSM
Title: A posteriori error estimation for finite element approximations of a PDE–constrained optimization problem in fluid dynamics.

- Cesar Naranjo, Mathematical Engineering and Master of Science. 2017
Advisors: Alejandro Allendes and Gabriel Barrenechea. 2017
Title: A divergence-free low-order stabilized finite element approximation for the steady-state Boussinesq problem.

- Esteban Cortés, Mathematical Engineering and Master of Science. 2017
Advisor: Alejandro Allendes. UTFSM
Title: Fully computable a posteriori error bounds for stabilized FEM approximations of nonstationary convection-reaction-diffusion problems.

- Gilberto Campaña, Master of Science. 2013
Advisor: Alejandro Allendes and Erwin Hernández. UTFSM
Title: Pointwise error estimations for a generalized Oseen problem and its application to an optimal control problem.

- Francisco Durán, Computer Engineering. 2013
Advisor: Alejandro Allendes. UTFSM
Title: Adaptive finite element algorithms for singularly perturbed equations.

- Gilberto Campaña, Mathematical Engineering. 2012
Advisor: Alejandro Allendes and Erwin Hernández. UTFSM
Title: A finite element approximation of an optimal control problem of the Stokes equations.

- Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE2019), Universidad de Concepción, Chile. Title: Stabilized finite element approximation for a generalized Boussinesq problem: a posteriori error analysis.
- International Conference on Boundary and Interior Layers BAIL 2018, University of Strathclyde, Glasgow, UK. Title: A posteriori error estimates for the Stokes problem with singular sources.
- XXXI Jornada de Matemática de la Zona Sur, Universidad Austral de Chile, Chile. Title: A posteriori error estimates for the Stokes problem with singular sources, 2018.
- The 27th Biennial Numerical Analysis Conference, Glasgow, UK. Title: A posteriori error estimation for optimal control problems in fluid dynamics, 2017.
- Primer encuentro conjunto de la Sociedad de Matemática de Chile (SOMACHI) y la Unión Matemática Argentina (UMA), SUMA, V Región, Chile ( 2016). Title: A posteriori error estimation for finite element approximations of optimal control problems.
- XXIX Jornada de Matemática de la Zona Sur, Santa Cruz, VI Región, Chile (2016). Title: Fully computable error estimation for Stabilized AFEM approximations of control constrained optimal control problems.
- 4 ta Escuela del Doctorado en Matemática de Valparaíso, UTFSM (2015). Title: Análisis numérico para control óptimo de ecuaciones diferenciales parciales.
- 26th Biennial Conference on Numerical Analysis, University of Strathclyde, Glasgow, UK, (2015). Title: A robust numerical method for a control problem of singularly perturbed equations.
- Valparaíso’s Mathematics and Applications Days (V-MAD V), Instituto de Mate- mática, PUCV (2015). Title: An adaptive stabilized method for the Navier–Stokes equations in three dimensions.
- Valparaíso’s Mathematics and Applications Days (V-MAD IV), Instituto de Mate- mática, PUCV (2014). Title: Adaptive finite element approximations for fluid flow problems.
- Workshop Métodos Numéricos de Ecuaciones Diferenciales (2013), Universidad de Salamanca. Title: Right inverse of the divergence operator and its application to the a posteriori error analysis for conforming finite element approximations.
- WONAPDE 2013, Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations, Universidad de Concepción. Title: Fully computable a posteriori error bounds for stabilized FEM approximations of convection-reaction-diffusion problems in three dimensions.
- Valparaíso’s Mathematics and Applications Days (V-MAD III), Instituto de Mate- mática, PUCV (2012). Title: Right inverse of the divergence operator an its application to the a posteriori error analysis for finite element approximations.
- Somachi 2012, Sociedad Matemática de Chile. Título: Right inverse of the divergence operator an its application to the a posteriori error analysis for finite element approximations.
- XI Jornada de Mécanica Computacional, Universidad Técnica Federico Santa María (2012): Title: Estimadores de error completamente computables y adaptividad para métodos de elementos finitos.
- Caleta Numérica (2012): Seminar on Numerical Analysis and Applied Mathematics at Valparaíso, Pontificia Universidad Católica de Valparaíso. Title: Estimadores de error completamente computables para métodos conformes de elementos finitos estabilizados.
- Seminario de Investigación en Ingeniería Mecánica (2012), Universidad Técnica Federico Santa María, Chile. Title: Estimaciones de error a posteriori para Métodos de Elementos Finitos.
- Seminario di Modellistica Differenziale Numerica (2011), Sapienza Università di Roma. Title: Computable a posteriori error bounds for the Stokes problem.
- 24 th Biennial Conference on Numerical Analysis 2011, Department of Mathematics and Statistics, University of Strathclyde, Scotland. Title: On the adaptive selection of the parameter in stabilized finite element approximation.
- Santiago Numérico 2 (2010), Quinto Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, Department of Mathematics, Pontificia Universidad Católica de Chile. Title: Computable error bounds for Stabilized finite element methods for the Stokes problem.
- Maths 2010 BMC/BAMC, British Mathematical Colloquium and British Applied Mathematics Colloquium, Maxwell Institute for Mathematical Sciences, Edinburgh. Title: Computable error bounds for nonconforming Fortin–Soulie finite element approximation of the Stokes problem.