Numerical Analysis of Partial Differential Equations; Finite Element Methods; Fluid and Solid Mechanics

Postdoc supervisions

Carlos Garcia, Doctor en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Subject: Numerical Analysis of conservative mixed formulations for Navier-Stokes and related problems.
Period: September 2017- September 2018.

PhD Students

Paulo Zuñiga, Doctorado en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Title of the thesis: High-Order Mixed Methods in Continuum Mechanics.
Co-advised with M. Solano
Defended: December 2019.

Sergio Caucao, Doctorado en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Title of the thesis: Mixed Finite Element Methods for Nonlinear Coupled Problems in Porous Media and Non-Isothermal Flows.
Co-advised with G.N. Gatica
Defended: December 2017.

Eligio Colmenares, Doctorado en Ciencias Aplicadas c/m en Ingeniería Matemática, Universidad de Concepción.
Title of the thesis: Mixed Finite Element Methods for Boussinesq, Navier-Stokes and Related Problems in Fluid Mechanics.
Co-advised with G.N. Gatica
Defended: December 2016.

Master Students

Nathalie Valenzuela, Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Augmented-mixed FEM for the Navier-Stokes/Darcy coupled problem with Beavers-Joseph-Saffman condition.
Co-advised with G.N. Gatica
Defended: August 2018.

Miguel Serón , Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: A fully Hdiv--conforming method for the stationary Boussinesq problem
Defended: September 2017.

Nestor Sánchez , Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Analysis of an augmented mixed-FEM for the Navier-Stokes-Brinkman problem
Co-advised with L.F. Gatica
Defended: August 2016.

Paulo Zuñiga , Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Aspectos computacionales de un metodo de elementos finitos para el problema de Boussunesq generalizado.
Defended: October 2015.

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 J. Camaño
Defended: September 2015.

Sergio Caucao, Magíster en Matemática c/m Matemática Aplicada, Universidad del Bío-Bío.
Title of the thesis: Análisis de un método de elementos finitos mixtos para el problema de Stokes con densidad variable en formulación pseudostress-velocidad.
Co-advised with D. Mora
Defended: March 2014.

Undergraduate students

Javier Almonacid, Ingeniería Civil Matemática, Universidad de Concepción.
Title of the thesis: Numerical analysis of a mixed finite element method for the Boussinesq equations with variable viscosity.
Co-advised with G. N. Gatica
Defended, August 2017.

Ramiro Rebolledo, Ingeniería Civil Matemática, Universidad de Concepción.
Title of the thesis: Análisis Numérico de una Formulación Mixta Aumentada para el Acoplamiento de Fluidos Quasi-Newtonianos con Medios Porosos.
Co-advised with G. N. Gatica
Defended, July 2013.

Presentations in international meetings (since 2014)

1. Conservative discontinuous finite volume and mixed schemes for a new four-field formulation in poroelasticity. WONAPDE 2019, Concepción, Chile. January 2019.
2. Error analysis of an augmented mixed method for the Navier-Stokes problem with mixed boundary conditions Santiago Numerico III . Santiago, Chile. June 2017
3. A fully-mixed finite element method for the Navier-Stokes/Darcy coupled problem with nonlinear viscosity MAFELAP 2016. Uxbridge, UK. June 2016
4. Locking-free finite element methods for poroelasticity. WONAPDE 2016, Concepción, Chile. January 2016.
5. Augmented mixed-FEM for Navier-Stokes and related problems in Fluid Mechanics. Advances in Discontinuous Galerkin Methods and Related Topics, Heidelberg, Germany. December 2015
6. A conforming mixed finite element method for the Navier-Stokes/Darcy coupled problem. Interpore 2015. Padova, Italy. May 2015
7. Analysis of an augmented mixed-FEM for the Navier-Stokes problem La Serena Numerica II, La Serena, Chile. January 2015.
8. A priori and a posteriori error analysis for a vorticity-based mixed finite element formulation for the generalized Stokes equations LANUS-FEM, Puerto Varas, Chile. September 2014.

Event Organization:

1. Numerical Analysis and Mathematical Modelling Seminar, Center for Research in Mathematical Engineering (Ci2MA: Centro de Investigacion en Ingenieria Matematica), Chile. Since 2011.
2. Third Spring school of Applied Mathematics (Tercera Escuela de Primavera de Matemática Aplicada EPRIMA), Universidad del Bio-Bio, Chile, October 19-23, 2020.
3. Second Spring school of Applied Mathematics (Segunda Escuela de Primavera de Matemática Aplicada EPRIMA), Universidad del Bio-Bio, Chile, October 14-18, 2019.
4. WONAPDE 2019, Sixth Chilean Workshop on Numerical Analysis of Partial Differential Equations. Universidad de Concepción, Chile. January 21-25, 2019.
5. First Spring school of Applied Mathematics (Primera Escuela de Primavera de Matemática Aplicada EPRIMA), Universidad del Bio-Bio, Chile, November 12-16, 2018.
6. Santiago Numérico III, Ninth Meeting on Numerical Analysis of Partial Differential Equations. Valparaiso, Chile, Santiago, Chile, June 28 - 30, 2017
7. La Serena Numérica II, Eighth Meeting on Numerical Analysis of Partial Differential Equations. Valparaiso, Chile, La Serena, Chile, January 14 - 16, 2015
8. Valparaiso Numérico IV, Seventh Meeting on Numerical Analysis of Partial Differential Equations. Valparaiso, Chile, December 11 - 13, 2013

Research Visits:

1. Department of Mathematics, University of Trento, Italy, August, 2019 (1 week)
1. Mathematical Institute, Oxford University, UK, June, 2019 (1 week)
2. Mathematical Institute, Oxford University, UK, June, 2016 (1 week)
3. Department of Mathematical Sciences, Loughborough University, UK, June, 2016 (1 week)
4. Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic, April-May, 2015 (3 week)
5. Faculty of Mathematics and Physics, Charles University in Prague, Prague, Czech Republic, June-July, 2014 (2 week)
6. Laboratori de Calcul Numeric (LaCaN), Universitat Politecnica de Catalunya, Barcelona, Spain, June 2014 (1 week)
7. Laboratori de Calcul Numeric (LaCaN), Universitat Politecnica de Catalunya, Barcelona, Spain, June 2013 (1 week)
8. Department of Mathematical Sciences, University of Delaware, Newark, DE, USA, February 2011 (1 month).
9. School of Mathematics, University of Minnesota, Minneapolis, MN, USA, September-December 2009 (3 months).
10. School of Mathematics, University of Minnesota, Minneapolis, MN, USA, October-November 2008 (2 months).