Least-Squares and DPG methods for eigenvalue approximations
Friday, February 26, 2021
10AM – 11AM
Accurate flux approximations are of interest in many applications and a lot of attention has recently been devoted to the reconstruction of the flux from a primal formulation since they are usually not H(div)-conforming. The reconstruction procedures for fluxes are also of particular importance for a posteriori error estimation and have a long history. An alternative approach uses flux-based variational formulations involving the flux as an independent variable approximated in a suitable H(div)-conforming finite element spaces. Such approaches may either lead to a saddle-point problem or a symmetric positive definite system. This talk focuses on the second type and covers the Least-Squares Method and the discontinuous Petrov-Galerkin method. Even if the proposed methods may not be competitive with other solution techniques, the presented analysis should shed some light on the fundamental properties of these formulations.
Fleurianne (Fleur) Bertrand obtained her Ph.D. in Mathematics from the University of Hannover in 2014 after working on the numerical analysis of two-phase flows. She was then Post-Doc at the University of Duisburg-Essen and started to apply her techniques in the numerical analysis and solution of partial differential equations to the field of solid mechanics. In 2018, she was appointed to a Junior professorship at the Humboldt Universität zu Berlin and continued the study of mixed finite element methods. In 2020, she took a position as assistant professor at the University of Twente on the mathematical theory of finite element methods.
(The Babuška Forum series was started by Professor Ivo Babuška several years ago to expose students to interesting and curious topics relevant to computational engineering and science with technical content at the graduate student level (i.e. the focus of the lectures is on main ideas with some technical content). Seminar credit is given to those students who attend.)