Numerical Treatment of PDEs, Finite Element Method, Boundary Element Method, FEM-BEM-coupling Methods Numerical methods for variational inequalities Preconditioning of adaptive BEM, FEM Discontinuous Petrov-Galerkin methods Least-squares methods

-) Supervision of Master thesis:
o) Adaptive BEM und FEM-BEM-Kopplung für die Lamé-Gleichung (Gregor Mitscha-Eibl), Master's thesis, Vienna University of Technology, 2014. (Supervised by Dirk Praetorius and Thomas Führer)
o) DPG methods for Stokes problem (José Carvajal), Master's thesis, PUC, since 03/2020
-) Supervision of PhD thesis:
o) DPG methods for the quad-curl problem (Pablo Herrera), PhD thesis, PUC, since 01/2020 (together with Norbert Heuer)

Charlas en congresos cientificos y charlas invitadas:
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2019
[46] DPG for plate bending, part II, 6th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2019. (21.01--25.01, Concepción, Chile)
[45] Problema de obstáculo y aproximaciones, Seminario Caleta Numérica, 2019. (11.10, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile)
[44] Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two, Reliable Methods of Mathematical Modeling (RMMM) 2019, 2019. (09.09-13.09, TU Wien, Vienna, Austria)
[43] A least-squares finite element method for the obstacle problem, The mathematics of finite elements and applications (MAFELAP) 2019, 2019. (18.06-21.06, Brunel University, London, Great Britain)
[42] Introduction to the DPG method: Abstract framework and applications, Partial Differential Equations Seminar, 2019. (26.06, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal)
[41] Ultraweak formulation of linear elliptic PDEs in nondivergence form and DPG approximation, Minimum Residual & Least-Squares Finite Element Methods 2019, 2019. (16.09-18.09, Humboldt-Universität zu Berlin, Berlin, Germany)
[40] Problemas Bi-Laplacianos -- Formulaciones variacionales, trazas y aproximaciones, Coloquio de Mátematica, Facultad de Matemáticas, 2019. (12.04, Pontificia Universidad Católica de Chile, Santiago, Chile)
2018
[39] On the DPG method for Signorini problems, 13th World Congress in Computational Mechanics, 2018. (22.07--27.07, New York, USA)
[38] Superconvergence in a DPG method for an ultra-weak formulation, Symposium Numerical PDE, 2018. (25.01, Pontificia Universidad Católica de Chile, Santiago, Chile)
[37] Problema de obstáculo y aproximaciones, Seminario de divulgación, IMC, 2018. (18.04, Pontificia Universidad Católica de Chile, Santiago, Chile)
[36] A Least-Squares method for the Obstacle Problem, XXXI Jornada de Matemática de la Zona Sur, 2018. (25.04-27.04, Universidad Austral de Chile, Valdivia, Chile)
[35] On the coupling of DPG and BEM, Symposium of the International Association for Boundary Element Methods (IABEM), 2018. (26.06--28.06, Paris, France)
[34] Superconvergent DPG methods for second order elliptic problems, Computational Methods in Applied Mathematics: CMAM-8, 2018. (03.07--05.07, Raubichi Sports Complex, Belarus)
[33] Stable multilevel splittings in __MATH0__, The Second Chilean Symposium on Boundary Element Methods (invited talk), 2018. (14.12, Valparaíso, Chile)
2017
[32] A linear Uzawa-type solver for nonlinear transmission problems, Encuentro anual de SOMACHI, 2017. (02.11-04.11, Universidad de Talca, Talca, Chile)
[31] On the DPG method for Signorini problems, Santiago Numérico III, 2017. (28.06-30.06, PUC, Santiago, Chile)
[30] Superconvergence in the DPG method with ultra-weak formulation, Minimum Residual & Least-Squares Finite Element Methods, 2017. (02.10-04.10, Portland State University, Portland, USA)
[29] A linear Uzawa-type solver for nonlinear transmission problems, BEM on the Saar 2017, 2017. (29.05-31.05, University of Saarbrücken, Saarbrücken, Germany)
[28] On the DPG method for Signorini problems, Austrian Numerical Analysis Day, 2017. (04.05-05.05, Paris Lodron University of Salzburg, Salzburg, Austria)
2016
[27] On the coupling of DPG and BEM, 5th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2016. (11.01-15.01, Concepción, Chile)
[26] El método DPG: Introducción y Extensiones, Seminario Ingeniería PUC (invited talk), 2016. (31.08, PUC, Santiago, Chile)
[25] Robust coupling of DPG and BEM for a singularly perturbed transmission problem, The mathematics of finite elements and applications (MAFELAP) 2016, 2016. (14.06-17.06, Brunel University, London, Great Britain)
[24] Sobre el acomplamiento de DPG con BEM, XXIX Jornada de Matemática de la Zona Sur, 2016. (21.04-23.04, Universidad de Talca, Santa Cruz, Chile)
[23] Robust coupling of DPG and BEM for a singularly perturbed transmission problem, International Conference on Boundary and Interior Layers (BAIL) 2016, 2016. (14.08-19.08, CSRC, Beijing, China)
[22] On the coupling of DPG and BEM, The First Chilean Symposium on Boundary Element Methods (invited talk), 2016. (14.12, PUC, Santiago, Chile)
2015
[21] A wirebasket preconditioner for the mortar boundary element method, Caleta Numérica (invited talk), 2015. (12.06, PUCV, Valparaíso, Chile)
[20] Multilevel methods for the hypersingular integral equation on locally refined triangulations, La Serena Numérica II, 2015. (14.01-16.01, La Serena, Chile)
[19] A wirebasket preconditioner for the mortar boundary element method, Seminar (invited talk), 2015. (09.06, Universidad del Bío Bío, Concepción, Chile)
[18] Optimal preconditioning for the coupling of adaptive FEM and BEM, 1st Pan-American Congress on Computational Mechanics (PANACM 2015), 2015. (27.04-29.04, Buenos Aires, Argentina)
[17] DPG method with optimal test functions for a fractional advection diffusion equation, XXIV Congreso de Matemática CAPRICORNIO (COMCA 2015), 2015. (05.08-07.08, Iquique, Chile)
2014
[16] Optimal preconditioning for the coupling of adaptive FEM and BEM, 12th Workshop on Fast Boundary Element Methods in Industrial Applications, 2014. (25.09-28.09, Hirschegg/Kleinwalsertal, Austria)
[15] Optimal preconditioning for the coupling of adaptive FEM and BEM, Seminar (invited talk), 2014. (11.09, Leibniz Universität Hannover, Hannover, Germany)
[14] Coupling of FEM and BEM: adaptivity and preconditioning, Seminar (invited talk), 2014. (20.11, TU Graz, Graz, Austria)
[13] Optimal preconditioning for the coupling of adaptive finite elements and boundary elements, 11th World Congress on Computational Mechanics (WCCM XI), 2014. (20.07-25.07, Barcelona, Spain)
[12] Efficient additive Schwarz preconditioning of the hypersingular integral equation on locally refined triangulations, Doctoral Program on Dissipation and Dispersion nPDEs (Seminar), 2014. (22.01, Vienna University of Technology, Austria)
2013
[11] Convergence of adaptive FEM-BEM coupling, 4th Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE), 2013. (14.01-18.01, Concepción, Chile)
[10] Efficient additive Schwarz preconditioning of the hypersingular integral equation on locally refined triangulations, 11th Workshop on Fast Boundary Element Methods in Industrial Applications, 2013. (26.09-29.09, Hirschegg/Kleinwalsertal, Austria)
[9] FEM-BEM couplings without stabilization, Symposium of the International Association for Boundary Element Methods (IABEM), 2013. (09.01-11.01, Santiago de Chile, Chile)
[8] Additive Schwarz methods for non-symmetric FEM-BEM couplings on locally refined meshes, Seminar (invited talk), 2013. (05.07, Leibniz Universität Hannover, Hannover, Germany)
[7] Stability of FEM-BEM couplings for nonlinear elasticity problems, 9th Austrian Numerical Analysis Day, 2013. (11.04-12.04, Graz, Austria)
2012
[6] FEM-BEM coupling without stabilization, 10th Workshop on Fast Boundary Element Methods in Industrial Applications, 2012. (27.09-30.09, Hirschegg/Kleinwalsertal, Austria)
[5] Convergence of adaptive FEM-BEM coupling driven by residual-based error estimators, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 2012. (10.09-14.09, Vienna, Austria)
[4] Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity, BEM on the Saar 2012, 2012. (12.05-16.05, Universität des Saarlandes, Saarbrücken, Germany)
[3] Classical FEM-BEM couplings: well-posedness, nonlinearities, and adaptivity, 8th Austrian Numerical Analysis Day, 2012. (10.05-11.05, Vienna University of Technology, Austria)
2010
[2] Computing the magnetostatic potential, Numerik-Statusseminar Ulm und Wien, 2010. (25.08-29.08, Kleinarl, Austria)
2009
[1] Computing the magnetostatic potential, Numerik-Statusseminar Ulm und Wien, 2009. (12.09-19.09, Cortona, Italy)