Finite elements: spectral problems; error estimates. Computational Mechanics: acoustic vibrations; fluid-structure interactions; thin structures; electromagnetism.

Ph.D. Advising:
- Luis M. Hervella-Nieto. Modal reduction and finite element methods for fluid-structure interaction problems. Ph.D. Thesis in Mathematics. Co-adviser: Alfredo Bermúdez. Universidade de Santiago de Compostela, Spain, 2000.
- Pablo Gamallo. Mathematical analysis of the simulation of elastoacoustic problems and active noise control. Ph.D. Thesis in Mathematics. Co-adviser: Alfredo Bermúdez. Universidade de Santiago de Compostela, Spain, 2002.
- Ana Alonso. A posteriori error estimates for the finite element solution of fluid-structure interaction vibration problems. Ph.D. Thesis in Mathematics. Universidad Nacional de La Plata, Argentina, 2002.
- Pilar Salgado. Mathematical and numerical analysis of some electromagnetic problems. Application to the simulation of metallurgical electrodes. Ph.D. Thesis in Mathematics. Co-adviser: Alfredo Bermúdez. Universidade de Santiago de Compostela, Spain, 2002.
- Duarte Santamarina. A contribution to the study of mathematical models in acoustics and fluid-structure interaction. Ph.D. Thesis in Mathematics. Co-adviser: Alfredo Bermúdez. Universidade de Santiago de Compostela, Spain, 2002.
- Erwin Hernández. Interaction between fluids and slender structures. Ph.D. Thesis in Mathematical Engineering. Universidad de Concepción, Chile, 2002.
- Galina C. García. Control and adaptivity in ocean circulation models. Ph.D. Thesis in Mathematical Engineering. Co-adviser: Axel Osses. Universidad de Concepción, Chile, 2004.
- Edwin M. Behrens. Numerical analysis of pollutant transport and degradation in aquatic media models. Ph.D. Thesis in Mathematical Engineering. Co-adviser: Rodolfo Araya. Universidad de Concepción, Chile, 2006.
- Andrés Prieto. Some contributions in time-harmonic dissipative acoustic problems. Ph.D. Thesis in Mathematics. Co-advisers: Alfredo Bermúdez and Luis M. Hervella-Nieto. Universidade de Santiago de Compostela, Spain, 2007.
- Ramiro M. Acevedo. Finite element methods for eddy currents problems. Ph.D. Thesis in Mathematical Engineering. Co-adviser: Salim Meddahi. Universidad de Concepción, Chile, 2008.
- Frank Sanhueza. Finite element methods for thin structures. Ph.D. Thesis in Mathematical Engineering. Co-adviser: Ricardo G. Durán. Universidad de Concepción, Chile, 2010.
- David Mora. Finite element methods for stability problems of thin structures. Ph.D. Thesis in Mathematical Engineering. Co-adviser: Carlo Lovadina. Universidad de Concepción, Chile, 2010.
- Carlos Reales. Numerical modeling of electromagnetic problems in metallurgy. Ph.D. Thesis in Mathematical Engineering. Co-advisers: Alfredo Bermúdez and Pilar Salgado. Universidad de Concepción, Chile, 2010.
- Bibiana López-Rodríguez. Numerical solution of electromagnetic forming problems. Ph.D. Thesis in Mathematical Engineering. Co-advisers: Alfredo Bermúdez and Pilar Salgado. Universidad de Concepción, Chile, 2012.
- Pablo Venegas. Contribution to the mathematical and numerical analysis of some electromagnetic problems. Ph.D. Thesis in Mathematical Engineering. Co-advisers: Alfredo Bermúdez and Dolores Gómez-Pedreira. Universidad de Concepción, Chile, 2013.
- Jessika Camaño. Finite element methods for problems in bioelectromagnetics. Ph.D. Thesis in Mathematical Engineering. Co-advisers: Alberto Valli and Ana Alonso-Rodríguez. Universidad de Concepción, Chile, 2013.
- Gonzalo Rivera. Virtual element method for spectral problems. Ph.D. Thesis in Mathematical Engineering. Co-advisers: David Mora and Lourenço Beirão da Veiga. Universidad de Concepción, Chile, 2016.
- Cinthya Rivas. Efficient computation of electromagnetic fields in solar cells. Ph.D. Thesis in Mathematical Engineering. Co-advisers: Manuel Solano and Peter Monk. Universidad de Concepción, Chile (in progress).
- Felipe Lepe. Acoustics, dissipation and vibration problems. Ph.D. Thesis in Mathematical Engineering. Co-advisers: David Mora y Salim Meddahi. Universidad de Concepción, Chile (in progress).

Postdoc Advising:
- Fabrice Jaillet. Former institution: Université Lyon I, France. Supported by Fundación Andes grant C-14055, Chile, November 2006 - July 2007.
- Ivana Sebestová. Former institution: Charles University, Prague, Czeck Republic. Supported by Anillo ANANUM ACT1118, CONICYT, Chile, June-October, 2014, and by FONDECYT 3150047, CONICYT, Chile, November 2014 - November 2016.

Selected lectures in conferences:
- Displacement F.E.M. without spurious solutions in vibration problems for fluid-structure coupled systems. Plenary Talk. ENIEF-95: IX Congreso sobre Métodos Numéricos y sus Aplicaciones, Bariloche, Argentina, 1995.
- Displacement F.E.M. without spurious solutions in vibration problems for fluid-structure coupled systems. Plenary Talk. Cuarto Congreso Franco-Latinoamericano de Matemáticas Aplicadas. Concepción, Chile, 1995.
- Modeling and numerical solution of damped elastoacoustic vibration problems. A. Bermúdez, R. Rodriguez, Plenary Talk. ENIEF-97: X Congreso sobre Métodos Numéricos y Aplicaciones. Bariloche, Argentina, 1997.
- Modeling and numerical solution of elastoacoustic vibrations with interface damping. A. Bermúdez, R. Rodriguez. Keynote lecture. IV WCCM: Fourth World Conference on Computational Mechanics. Buenos Aires, Argentina, 1998.
- Finite element approximation of a quadratic eigenvalue problem arising in damped fluidstructure interactions. A. Bermúdez, R. Durán, R. Rodriguez, J. Solomin. MAFELAP 1999: X Conference on Mathematical Aspects of Finite Elements and Applications, University of Brunel, UK, 1999.
- A finite element method to compute damped vibration modes in dissipative acoustics A. Bermúdez, R. Durán, R. Rodriguez, J. Solomin. ECCOMAS 2000. European Congress on Computational Methods in Applied Science and Engineering, Barcelona, Spain, 2000.
- A posteriori error estimates for fluid-structure vibration problems. A. Alonso, A. Dello Russo, C. Padra, R. Rodriguez. AMIF, Applied Mathematics for Industrial Flows, Il Ciocco, Italy, 2000.
- Finite element solution of a fluid-structure vibration problem. A. Bermúdez, R. Rodriguez. Invited speaker. ICRACM-2001: International Conference on Recent Advances in Computational Mathematics, Matsuyama, Japan, 2001.
- A finite element method for the eddy currents problem in an electrode with input intensities as boundary data. A. Bermúdez, R. Rodriguez, P. Salgado. Semiplenary lecture. MECOM 2002: First South-American Congress on Computational Mechanics. Paraná, Argentina, 2002.
- Numerical analysis of problems arising from the modeling of a metallurgical arc furnace. A. Bermúdez, R. Rodriguez, P. Salgado. Plenary Talk. XVII Jornadas de Matemática de la Zona Sur, Trailanqui, Chile, 2003.
- A posteriori error estimates for the finite element approximation of eigenvalue problems. R. Durán, C. Padra, R. Rodriguez. Chemnitz FEM-Symposium 2003, Chemnitz, Germany, 2003.
- A posteriori error analysis for a large-scale ocean circulation finite element model. J.M. Cascón, G.C. Garcia, R. Rodriguez. Keynote lecture. ADMOS 2003: Adaptive Modeling and Simulation, Göteborg, Sweden, 2003.
- Finite element methods in local active control of sound. A. Bermúdez, P. Gamallo, R. Rodriguez. Invited speaker. INMAT-2003: II Congreso Internacional de Matemática Aplicada a la Ingenieria y Enseñanza de la Matemática en Ingenieria. Buenos Aires, Argentina, 2003.
- Numerical analysis of some problems arising in the modeling of a metallurgical arc furnace. A. Bermúdez, R. Rodriguez, P. Salgado. WONAPDE-2004: First Workshop on Numerical Analysis of PDE, Concepción, Chile, 2004.
- A posteriori error analysis for the finite element approximation of fluid-structure interaction vibration problems. R. Durán, C. Padra, R. Rodriguez. Workshop on Self-Adaptive Methods for PDE, Mathematisches Forschungsinstitut, Oberwolfach, Germany, 2004.
- PML exact absorbing boundary conditions for the acoustic wave equation. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodriguez. Plenary talk. XV Congreso de Matemáticas Capricornio, COMCA, Antofagasta, Chile, 2005.
- PML exact absorbing boundary conditions for the acoustic wave equation. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodriguez. Plenary talk. UMA 2005, LV Reunión Anual de la Unión Matemática Argentina, Salta, Argentina, 2005.
- Exact bounded PML for the Helmholtz equation. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodriguez. Invited speaker. MNED 2005, Métodos Numéricos para Ecuaciones Diferenciales, Buenos Aires, Argentina, 2005.
- An exact bounded PML technique for the scattering of acoustic waves. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodriguez. Invited speaker. Thematic session on Numerical Analysis. ICAM 2006: International Congress on the Applications of Mathematics, Santiago, Chile, 2006.
- An exact bounded PML technique for the scattering of acoustic waves. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodriguez. Invited speaker. Variational Formulations in Mechanics: Theory and Applications, Laboratório Nacional de Computação Cientifica, Petrópolis, Brazil, 2006.
- A finite element method for the magnetostatic problem in terms of scalar potentials. A. Bermúdez, R. Rodriguez, P. Salgado. WONAPDE-2007: Second Workshop on Numerical Analysis of PDE, Concepción, Chile, 2007.
- Numerical approximation of the vibration modes of a Timoshenko curved rod of arbitrary geometry. R. Rodriguez, F. Sanhueza. Invited lecture. Thematic session on Numerical Analysis. UMA 2007, LVII Reunión Anual de la Unión Matemática Argentina, Córdoba, Argentina, 2007.
- Buckling of Reissner-Mindlin plates. C. Lovadina, D. Mora, R. Rodriguez. Invited lecture. Thematic session on Numerical Analysis. UMA 2008, LVIII Reunión Anual de la Unión Matemática Argentina, Mendoza, Argentina, 2008.
- Buckling of Reissner-Mindlin plates. C. Lovadina, D. Mora, R. Rodriguez. Keynote lecture. ENIEF 2008: XVII Congreso sobre Métodos Numéricos y sus Aplicaciones, San Luis, Argentina, 2008.
- A numerical method for an electromagnetic forming problem in axisymmetric domains. A. Bermúdez, C. Reales, R. Rodriguez, P. Salgado. Coupled Problems 2009: Computational Methods for Coupled Problems in Science and Engineering III, Ischia, Italy, 2009.
- Finite element model of an electromagnetic forming problem in axisymmetric domains. A. Bermúdez, C. Reales, R. Rodriguez, P. Salgado. Plenary lecture. Current & New Trends in Scientific Computing, CMM, Santiago, Chile, 2009.
- An efficient solver for a time-dependent eddy current problem in 3D. R. Acevedo, E. Behrens, S. Meddahi, R. Rodriguez. WONAPDE-2010: Third Workshop on Numerical Analysis of PDE, Concepción, Chile, 2010.
- Finite element solution of an eddy current time-dependent problem on moving domains arising from electromagnetic forming. A. Bermúdez, R. Muñoz, C. Reales, R. Rodriguez, P. Salgado. SIMAI-SEMA 2010, Cagliari, Italy, 2010.
- Numerical approximation of the spectrum of the curl operator. R. Rodriguez, P. Venegas. Plenary lecture. First Joint Meeting, Sociedad de Matemática de Chile - American Mathematical Society, Pucón, Chile, 2010.
- Analysis of an eddy current transient problem arising from the simulation of electromagnetic forming. A. Bermúdez, R. Muñoz, C. Reales, R. Rodriguez, P. Salgado. Plenary lecture. VIII Congreso Colombiano: Métodos Numéricos, Simulación en Ciencias y Aplicaciones Industriales, Medellin, Colombia, 2011.
- Spectral approximation of the curl operator. R. Rodriguez, P. Venegas. Invited speaker. NELIA 2011: Workshop on Numerical Electromagnetics and Industrial Applications, Santiago de Compostela, España, 2011.
- Spectral approximation of the curl operator. R. Rodriguez, P. Venegas. Invited speaker. Thematic session on Numerical Analysis. CLAM 2012, Córdoba, Argentina, 2012.
- Numerical approximation of Beltrami fields. R. Rodriguez, P. Venegas. Invited lecture. NAPDE: Numerical Analysis of PDE. Adaptivity, Error Control and Convergence. Gargnano del Garda, Italy, 2013.
- Spectral approximation of the curl operator in multiply connected domains. E. Lara, R. Rodriguez, P. Venegas. Invited lecture. Fluid Dynamics and Electromagnetism: Theory and Numerical Approximation. CIRM (Centro Internazionale per la Ricerca Matematica), Levico Terme, Italy, 2014.
- Finite element computation of Beltrami fields. R. Rodriguez. Semiplenary lecture. ENIEF 2014: XXI Congreso sobre Métodos Numéricos y sus Aplicaciones, Bariloche, Argentina, 2014.
- Finite element spectral approximation of the curl operator in multiply connected domains. R. Rodriguez. Semi-plenary speaker. Workshop C2: Foundation of Numerical PDE's. FoCM 2014: Foundation of Computational Mathematics, Montevideo, Uruguay, 2014.
- Finite element computation of force-free Beltrami fields. E. Lara, R. Rodriguez, P. Venegas. Semiplenary lecture. PANACM 2015: 1st. Pan-American Congress on Computational Mechanics, Buenos Aires, Argentina, 2015.
- Finite element spectral approximation of the curl operator in multiply connected domains. E. Lara, R. Rodriguez, P. Venegas. Semiplenary lecture. XX Congreso Colombiano de Matemáticas, Universidad Nacional de Colombia - Sede Manizales, Colombia, 2015.
- Finite element approximation of Beltrami fields in multiply connected domains. E. Lara, R. Rodriguez, P. Venegas. Minisimposium on Emerging PDEs: Analysis and Computation. ICIAM 2015: International Congress on Industrial and Applied Mathematics. Beijing,
China, 2015.
- Finite element spectral approximation of the curl operator in multiply connected domains. E. Lara, R. Rodriguez, P. Venegas. Invited lecture. Thematic session on Numerical Analysis. UMA 2015, LXIV Reunión Anual de la Unión Matemática Argentina, Santa Fe, Argentina, 2015.
- Residual-based a posteriori error estimator for the Maxwell's eigenvalue problem. R. Rodriguez, I. Sebestová. WONAPDE 2016: Fifth Workshop on Numerical Analysis of PDE, Concepción, Chile, 2016.
- Residual-based a posteriori error estimator for the Maxwell's eigenvalue problem. D. Boffi, L. Gastaldi, R. Rodriguez, I. Sebestová. AMFE 2016: Advances in Mathematics of Finite Elements, USACM/ICES, University of Texas, Austin, 2016.
- Residual-based a posteriori error estimator for the Maxwell's eigenvalue problem. D. Boffi, L. Gastaldi, R. Rodriguez, I. Sebestová. Invited lecture. Thematic session on Numerical Analysis of PDE. SUMA 2016: First Joint Meeting of Sociedad Matemática Chilena and Unión Matemática Argentina, Valparaiso, Chile, 2016.

Selected seminars:
- Asymptotically exact error estimators for finite element methods. Numerical Analysis Seminar, University of Maryland, College Park, USA, 1990.
- The quality assessment of finite element approximations. Instituto di Analisi Numerica, Università di Pavia, Italy, 1992.
- Asymptotically exact error estimators in the finite element method. Matematica, Università degli Studi di Milano, Italy, 1992.
- Vibration of media with fluid-structure interaction. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina, 1993.
- Finite element solution of vibration problems for coupled systems with fluid-structure interaction. Departamento de Matemática Aplicada. Universidade de Santiago de Compostela, Spain, 1995.
- Computation of the vibration modes of systems with fluid-structure interaction. Universidad de la Frontera, Temuco, Chile, 1997.
- Modeling and FE analysis of damped vibrations for fluid-structure coupled systems. Applied and Computational Math. Seminar, Penn. State University, State College, USA, 1999.
- Numerical analysis of a FEM to compute damped vibrations. Numerical Analysis Seminar, University of Maryland, College Park, USA, 1999.
- Modeling and computation of damped vibrations for fluid-structure interaction systems. Departamento de Matemática Aplicada y Computación. Universidad de Valladolid, Spain, 1999.
- Modeling and computation of damped vibrations for fluid-structure interaction systems. Seminario de Matemática Aplicada. Universidad de Santiago de Compostela, Spain, 1999.
- Analysis of a FEM for low-frequency harmonic Maxwell's equations. Instituto di Analisi Numerica, Università di Pavia, Italy, 2000.
- A finite element method to compute damped vibration modes in dissipative acoustics. Departamento de Matemática Aplicada. Universidad de Salamanca, Spain, 2001.
- A finite element method for the computation of damped vibration modes in dissipative acoustics. Departamento de Matemáticas. Universidad de A Coruña, Spain, 2002.
- Computing vibration modes of a fluid-plate coupled system. Laboratório Nacional de Computação Cientifica, Petrópolis, Brazil, 2003.
- Finite element techniques for active control of noise in enclosures. Laboratório Nacional de Computação Cientifica, Petrópolis, Brazil, 2003.
- Finite element analysis of an electromagnetic problem arising from the simulation of metallurgical electrodes. Programme Computational Challenges in PDEs. Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 2003.
- A finite element method for ocean circulation modeling. Departamento de Matemáticas. Universidad de A Coruña, Spain, 2004.
- Efficient finite element solution of pure Neumann problems. Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, Spain, 2005.
- Finite element methods for active noise control. Departamento de Matemática Aplicada II, Universidade de Vigo, Spain, 2005.
- An exact bounded perfectly matched layer for time-harmonic scattering problems. Instituto di Analisi Numerica, Università di Pavia, Italy, 2005.
- Finite element methods in active control of sound. Facultad de Ingenieria, Universidad Nacional de La Plata, Argentina, 2005.
- PML exact absorbing conditions for the wave equation. Departamento de Matemáticas, Universidad de Oviedo, España, 2007.
- Finite element methods in active control of sound. Departamento de Ingenieria Estructural y Geotécnica, Pontificia Universidad Católica de Chile, Santiago, Chile, 2007.
- Buckling of Reissner-Mindlin plates. Seminario de Matemática Aplicada. Universidad de Santiago de Compostela, Spain, 2009.
- Numerical approximation of Beltrami fields. Seminario de Matemática Aplicada. Universidad de Santiago de Compostela, Spain, 2009.
- Numerical approximation of the spectrum of the curl operator. Departamento de Matemática. Universidad Nacional, Sede Medellin, Colombia, 2011.
- Numerical approximation of Beltrami fields in multiply connected domains. Seminario SIMNUMAR, Departamento de Matemáticas, Facultade de Informática, Universidade da Coruña, Spain, 2015.
- An eddy current time-dependent problem on moving domains arising from electromagnetic forming. Department of Applied Mathematics, Communication University of China, Beijing, China, 2015.
- Finite element spectral approximation of the curl operator in multiply connected domains. Department of Applied Mathematics, Communication University of China, Beijing, China, 2015.
- Residual-based a posteriori error estimator for the Maxwell's eigenvalue problem. Seminario de Matemática Aplicada, Universidade de Santiago de Compostela, España, 2016.

Selected short courses:
- Environmental Modeling: Quality Models for Water River Systems (10 hours). Summer School on Environmental Science, Centro de Ciencias Ambientales EULA-Chile, Universidad de Concepción, Chile, 2003.
- Finite Element Methods for Fluid-Structure Vibration Problems (10 hours). V Winter School Luis A. Santaló, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina, 2012.
- Finite Element Numerical Solution of Partial Differential Equations (12 hours). Escuela de Matemática de América Latina y el Caribe (EMALCA), Universidad Nacional de la Patagonia San Juan Bosco, Puerto Madryn, Argentina, 2012.
- Finite Element Numerical Solution of Partial Differential Equations (12 hours). Escuela de Matemática de América Latina y el Caribe (EMALCA), Universidad de Costa Rica, Sede del Atlántico, Turrialba, Costa Rica, 2014.
- Numerical Approximation of Low-Frequency Problems (7 hours). Summer School of CIME (Centro Internazionale Matematico Estivo) on Computational Electromagnetism, Cetraro, Italy, 2014.
- The Spectral Problem for the Curl Operator (3 hours). VIII Encontro Nacional de Análise Matemática e Aplicações, ENAMA-2014, Universidade Federal de Pernambuco, Recife, Brazil, 2014.