Numerical Analysis of Partial Differential Equations

PhD. Theses

Miguel Serón,
Doctorado en Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Conforming and non-conforming discretizations for desalination process models.
Co-advised with R. Oyarzúa and M. Solano
Defended: April 2025.

Isaac Bermúdez,
Doctorado en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Title of the thesis: Discontinuous Galerkin methods for interface problems: application to water desalination processes.
Co-advised with M. Solano
Defended: January 2025.

Eduardo De Los Santos,
Doctorado en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Title of the thesis: Divergence-free finite elements en general topological domains and applications.
Co-advised with A. Alonso Rodríguez
and R. Rodríguez
Defended: March 2019.

Master Theses

Katherine Rojo,
Magíster en Matemática Aplicada, Universidad Católica de la Santísima Concepción.
Title of the thesis: Métodos de elementos finitos mixtos basado en paseudoesfuerzo conservativo de momentum y de masa para problemas de flujo de fluidos.
Co-advised with R. Oyarzúa.
Defended: April 2025.

Lady Ángelo,
Magíster en Matemática Aplicada, Universidad Católica de la Santísima Concepción.
Title of the thesis: Análisis Numérico de una Formulación Mixta para Flujos Magnetohidrodinámicos Estacionarios en Medios Porosos.
Co-advised with S. Caucao
Defended: June 2023.

Cristian Muñoz,
Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Analysis of a mixed finite element method for the Poisson problem with data in L^p, 2n/(n + 2) < p < 2, n = 2,3.
Co-advised with R. Oyarzúa
Defended: September 2015.

Undergraduate Theses

Felipe Vargas,
Ingeniería Civil Matemática, Universidad de Concepción.
Title of the thesis: Estimación a posteriori del error y esquemas adaptativos para la solución por elementos finitos de problemas de electroencefalografía.
Co-advised with R. Rodríguez
Defended: January 2014.

PRESENTATIONS AT CONFERENCES

2024

July 21-26, WCCM-PANACM 2024: 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics, held at Vancouver, British Columbia, Canada.
Title: Analysis of a FEM with exactly divergence-free magnetic field for the stationary MHD problem.
(co-authors: A. Alonso Rodríguez, R. Oyarzúa)

June 3-7, ECCOMAS 2024: 9th European Congress on Computational Methods in Applied Sciences and Engineering, held at Lisboa, Portugal.
Title: A conforming finite element method for a nonisothermal fluid-membrane interaction.
(co-authors: R. Oyarzúa, M. Serón, M. Solano)

April 24-26, JMZS 2024: XXXVI Jornada de Matemática de la Zona Sur, held at Universidad Católica de Temuco, Temuco, Chile.
Title: A Conforming and Mass Conservative Pseudostress-Based Mixed Finite Element Method for Stokes.
(co-author: R. Oyarzúa)

January 15-19, WONAPDE 2024: Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations, held at Universidad de Concepción, Concepción, Chile.
Title: A five-field mixed formulation for stationary magnetohydrodynamic flows in porous media.
(co-authors: L. Ángelo, S. Caucao)

2023

September 6 - 8, MASC+ Workshop: Major Advances in numerical Schemes for Conservation laws + other topics Workshop on the ocassion of Mauricio Sepúlveda's 60th Birthday, held at Nevados de Chillán, Chillán, Chile.
Title: Numerical Analysis of a Mixed Formulation for Stationary Magnetohydrodynamic Flows in Porous Media.
(co-authors: L. Ángelo, S. Caucao)

August 20 - 25, ICIAM 2023: 10th International Congress on Industrial and Applied Mathematics, held at Waseda University, Tokyo, Japan.
Title: A five-field mixed formulation for stationary magnetohydrodynamic flows in porous media.
(co-authors: L. Ángelo, S. Caucao)

August 14 - 18, ICOSAHOM 2023: International Conference on Spectral and High Order Methods, held at Yonsei University, Seoul, Korea.
Title: A conforming and divergence-free approximation for the pseudostree-based formulation of the Stokes problem.
(co-author: R. Oyarzúa)

2022

August 29 - September 2, CMAM 2022: 9th International Conference on Computational Methods in Applied Mathematics, held at TU Wien, Wien, Austria.
Title: Analysis of a conforming and mass-conservative mixed-fem for the Stokes problem.
(co-author: R. Oyarzúa)

2021

September 13-17, CLAM VI 2021: VI Congreso Latinoamericano de Matemáticos (CLAM) 2021, held at Montevideo, Uruguay.
Title: A priori and a posteriori error analysis of a momentum conservative mixed–FEM for the stationary Navier–Stokes problem.
(co-authors: S. Caucao, C. García, R. Oyarzúa, S. Villa)

July 28-30, COMCA 2021: XXIX Congreso de Matemáticas Capricornio, held at Universidad de Atacama, Chile.
Title: A new algorithm for the approximations of the spectrum of the curl operator.
(co-authors: A. Alonso Rodríguez)

2019

September 24-27, SUMA 2019: Reunión Anual de la Unión Matemática Argentina y de la Sociedad Matemática Chilena, held at Universidad Nacional de Cuyo, Mendoza, Argentina.
Title: Analysis of a momentum conservative mixed-FEM for the stationary Navier-Stokes problem.
(co-authors: C. García, R. Oyarzúa)

July 31- August 2, COMCA 2019: XXVIII Congreso de Matemáticas Capricornio, held at Universidad de La Serena, La Serena, Chile.
Title: Analysis of a momentum conservative mixed-FEM for the stationary Navier-Stokes problem.
(co-authors: C. García, R. Oyarzúa)

January 21-25, WONAPDE 2019: Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations, held at Universidad de Concepción, Concepción, Chile.
Title: Analysis of a mixed FEM for stationary incompressible magneto-hydrodynamics.
(co-authors: C. García, R. Oyarzúa)

2017

June 28-30, Santiago Numérico III: Noveno Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, held at Pontificia Universidad Católica de Chile, Santiago, Chile.
Title: An augmented stress-based mixed finite element method for the Navier-Stokes equations with nonlinear viscosity.
(co-authors: G. Gatica, R. Oyarzúa, R. Ruiz-Baier)

May 15-19, 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation: WAVES 2017, held at University of Minnesota, Twin Cities, EEUU.
Title: Electromagnetic Stekloff Eigenvalues in Inverse Scattering.
(co-authors: C. Lackner, P. Monk)

April 26-28, XXX Jornada de Matemática de la Zona Sur, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Graphs, spanning trees and divergence-free finite elements in domains of general topology.
(co-authors: A. Alonso, R. Ghiloni, A. Valli)

2016

August 2-5, COMCA 2016: XXV Congreso de Matemáticas Capricornio, held at Universidad Católica del Norte, Antofagasta, Chile.
Title: A priori and a posteriori error analyses of a flux-based mixed-FEM for convection-diffusion-reaction problems.
(co-authors: L.F. Gatica, R. Oyarzúa)

June 14-17, Brunel MAFELAP 2016, held at Brunel University, Uxbridge, United Kingdom.
Title: Numerical approximation of the spectrum of the curl operator in multiply connected domains.
(co-authors: A. Alonso, R. Rodríguez, A. Valli, P. Venegas)

April 21-23, XXIX Jornada de Matemática de la Zona Sur, held at Universidad de Talca, Santa Cruz, VI Región, Chile.
Title: Analysis of a dual-mixed formulation on nonstandard Banach spaces.
(co-authors: C. Muñoz, R. Oyarzúa)

January 11-15, WONAPDE 2016: Fifth Chilean Workshop on Numerical Analysis of Partial Differential Equations, held at Universidad de Concepción, Concepción, Chile.
Title: Numerical approximation of the spectrum of the curl operator in multiply connected domains.
(co-authors: A. Alonso, R. Rodríguez, A. Valli, P. Venegas)

2015

August 5-7, COMCA 2015: XXIV Congreso de Matemáticas Capricornio, held at Universidad Arturo Prat, Iquique, Chile.
Title: An augmented mixed finite lement method for the Navier-Stokes equations with variable viscosity.
(co-authors: G.N. Gatica, R. Oyarzúa, G. Tierra)

April 27-29, PANACM 2015: First Pan-American Congress on Computational Mechanics, held at Buenos Aires Hilton Hotel, Buenos Aires, Argentina.
Title: Analysis of an augmented mixed-FEM for the Navier-Stokes problem.
(co-authors: R. Oyarzúa, G. Tierra)

2014

September 3-5, LANUS-FEM: Latest Advances in Numerical Solutions with FEM, held at Hotel Cumbres, Puerto Varas, X Región, Chile.
TItle: Assessment of two approximation methods for the inverse problem of electroencephalography.
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

July 7, Necas Seminar on Continuum mechanics, held at the Mathematical Institute of the Charles University, Praga, República Checa.
Title: An adaptive strategy to solve the inverse problem of electroencephalography.
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

April 23-25, XXVII Jornada de Matemática de la Zona Sur, held at Trailanqui, IX Región, Chile.
Title: Analysis of an augmented mixed finite element method for the Stokes-Darcy coupled problem.
(co-authors: G. N. Gatica, R. Oyarzúa, R. Ruiz-Baier, P. Venegas)

2013

December 11-13, VALPARAISO NUMERICO IV: Séptimo Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, held at Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
Title: Comparison of two computational models for the inverse problem of electroencephalography.
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

November 7-9, LXXXII Encuentro Anual de la Sociedad Matemática de Chile SOMACHI, held at Olmué, Valparaíso, Chile.
Title: Assessment of two approximation methods for the inverse problem of electrostatics with a dipole source
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

January 14-18, WONAPDE 2013: Fourth Chilean Workshop on Numerical Analysis of Partial Differential Equations, held at Universidad de Concepción, Concepción, Chile.
Title: An a posteriori error estimator for the electrostatics problem with a current dipole source.
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

January 3-5, Workshop Coupled Physics Inverse Problems CPIP2013, held at Universidad de Chile, Santiago, Chile.
Title: Inverse source problems for eddy current equations.
(co-authors: A. Alonso, A. Valli)

2012

October 4, XXXVIII Semana de la Matemática, held at Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
Title: A posteriori error estimates for the electrostatics problem.
(co-authors: A. Alonso, R. Rodríguez, A. Valli)

January 5, Second CI2MA Focus Seminar: Computational Electromagnetism, held at Universidad de Concepción, Concepción, Chile.
Title: Inverse source problems for eddy current equations.
(co-authors: A. Alonso, A. Valli)

2011

December 14-16, LA SERENA NUMERICA I: Sexto Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, held at La Serena, Chile.
Title: Inverse source problems for eddy current equations.
(co-authors: A. Alonso, A. Valli)

2010

December 9-11, SANTIAGO NUMERICO II: Quinto Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, held at Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile.
Title: Well-posedness and error estimates of a hybrid formulation for the eddy current problem.
(co-author: R. Rodríguez)

TALKS AND SEMINARS

2024

June 2024, DIM-CMM PDE Seminar, Universidad de Chile, Santiago, Chile. Online.
Title: Analysis of a mixed FEM for Stationary Magnetohydrodynamic Flows in Porous Media.

April 2024, Semana Nacional de la Matemática - Jugando con las Matemáticas en la UCSC held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Simulación de la vida real: un tema tanto para hombres como mujeres.

2023

June 2023, Seminario de Investigación ModeMat, Escuela Politécnica Nacional, Quito, Ecuador. Online.
Title: Numerical Analysis of a Mixed Formulation for Stationary Magnetohydrodynamic Flows in Porous Media.

April 2023, Seminario Grupo Medicina Computacional, Pontificia Universidad Católica de Chile. Online.
Title: Análisis Numérico para problemas de electroencefalografía y de mecánica de fluidos.

2022

November 2022, Workshop en Matemática Multidisciplinar UBB, held at Universidad del Bío-Bío, Concepción, Chile.
Title: Comparación de dos modelos computacionales para el problema inverso de la electroencefalografía.

November 2022, Serie de Seminarios IM+ICM 50 años, held at Universidad de Concepción, Concepción, Chile.
Title: Analysis of a new mixed-FEM for stationary incompresible magneto-hydrodynamics.

September 2022, Seminar held at University of Trento, Trento, Italy.
Title: A conforming and divergence-free approximation for the pseudostress-based formulation of the Stokes problem.

August 2022, ENIM 2022: Encuentro Nacional de Ingeniería Matemática 2022, held at Pontificia Universidad Católica de Chile, Santiago, Chile.
Title: Introducción al Método de Elementos Finitos y una aplicación al Problema Inverso de la Electroencefalografía.

August 2022, Primer Workshop sobre Métodos Computacionales para procesos de Desalinización - DSALT 2022, held at Hotel Terrano, Concepción, Chile.
Title: Numerical Analysis of momentum conservative mixed finite element methods for Fluid flow problems.

January 2022, Escuela Emalca Virtual Chile: "Matemáticas y sus Aplicaciones". Online, organized by Centro de Modelamiento Matemático (CMM), Universidad de Chile, Santiago, Chile.
Title: Método de Elementos Finitos y algunas aplicaciones.

2021

November 2021, Summer School in Applied Mathematics EVMA 2021, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Comparación de dos modelos computacionales para el problema inverso de la electroencefalografía.

2020

January 2020, Summer School in Applied Mathematics EVMA 2020, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Aplicación de Métodos Numéricos para la Resolución de Problemas de la Vida Real.

2019

October 2019, Spring School in Applied Mathematics EPANUM 2019, held at Universidad de Concepción, Concepción, Chile.
Title: Introducción al Método de Elementos Finitos.

January 2019, Summer School in Applied Mathematics 2019, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Métodos numéricos para la resolución de problemas de la Física e Ingeniería.

2017

April 2017, Seminario del Departamento de Matemática y Física Aplicadas, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Finite element approximation of the spectrum of the curl operator in a multiply-connected domain.

January 2017, Summer School in Applied Mathematics EVMA 2017, held at Universidad Católica de la Santísima Concepción, Concepción, Chile.
Title: Análisis Matemático en R^n.

2016

August 2016, Coloquio de Matemáticas held at Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile.
Title: Finite element approximation of the spectrum of the curl operator in a multiply-connected domain.

2015

December 2015, Numerical Analysis and PDE Seminar held at University of Delaware, Newark, USA.
Title: A new augmented mixed finite element method for the Navier-Stokes problem.

November 2015, Numerical Analysis Seminar held at University of Maryland, College Park, USA.
Title: A new augmented mixed finite element method for the Navier-Stokes problem.

May 2015, Seminario de Análisis Numérico "Caleta Numérica" held at Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
Title: A new augmented mixed finite element method for the Navier-Stokes problem.

2014

November 2014, Seminario de Análisis Numérico y Modelación Matemática organized by GIMNAP-Departamento de Matemática, Universidad del Bío-Bío and the Mathematical Engineering Research Center, CI2MA, Universidad de Concepción.
Title: A new augmented mixed finite element method for the Navier-Stokes equations.

September 2014, Spring School in Applied Mathematics EPANUM 2014 held at Universidad de Concepción, Concepción, Chile.
Title: Comparison of some approximation methods for the inverse problem of EEG.

July 2014, Neças Seminar on Continuum Mechanics held at Mathematical Institute of the Charles University, Prague, Czech Republic.
Title: An adaptive strategy to solve the inverse problem of electroencephalography

2013

October 2013, Liceo la Asunción, Talcahuano, Chile.
Title: Algunos ejemplos interesantes de modelamiento matemático.

January 2013, Workshop Coupled Physics Inverse Problems CPIP2013 held at CMM, Universidad de Chile, Santiago, Chile.
Title: Inverse source problems for eddy current equations.

2012

October 2012, XXXVIII Semana de la Matemática held at Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
Title: A posteriori error estimates for the electrostatics problem.

January 2012, Second CI2MA Focus Seminar: COMPUTATIONAL ELECTROMAGNETISM held at Universidad de Concepción, Concepción, Chile.
Title: Inverse source problems for eddy current equations

EVENT ORGANIZATION

2024

WONAPDE 2024: Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations, held at Universidad de Concepción, Concepción, Chile.

2020

Summer School in Applied Mathematics EVMA 2020, Universidad Católica de la Santísima Concepcion, Concepcion, Chile.

2017

XXX Jornadas de la Matemática de la Zona Sur, Universidad Católica de la Santísima Concepción, Concepción, Chile.

Santiago Numérico III, Noveno Encuentro de Análisis Numérico de Ecuaciones Diferenciales Parciales, Pontificia Universidad Católica de Chile, Santiago, Chile.

2014

LANUS-FEM: Latest Advances in Numerical Solutions with FEM, On the Occasion of Rodolfo Rodríguez’s 60th Birthday, Puerto Varas, Chile.

RESEARCH VISITS

2024
Simon Fraser University, Vancouver, Canada. (1 week).

2022
Università di Trento, Trento, Italy (1 week).

2019
University of Trento, Trento Italy (3 weeks).

2016
Mathematical Institute, Oxford University, UK (1 week)

2015
Department of Mathematical Sciences, University of Delaware, Newark, USA (3 months)

2014
Mathematical Institute of the Charles University, Prague, Czech Republic (2 weeks)
University of Trento, Trento Italy (1 month).

2013
University of Trento, Trento Italy (3 months).

2012
University of Trento, Trento Italy (3 months).

2011
University of Trento, Trento Italy (2,5 months).