(EDG-) HDG methods for incompressible flows is the name of the talk that this Tuesday, January 14, delivered at the Faculty of Physical and Mathematical Sciences at Universidad de Concepcion, the academician of the Department of Applied Mathematics at the University of Waterloo (Canada), Sander Rhebergen.

“The error in the discrete velocity for many finite element methods for incompressible flow depends on the product of the best approximation error in the pressure and the inverse of the viscosity of the flow. As a result, the smaller the viscosity, the more degrees of freedom are required to achieve a certain level of accuracy in the velocity solution. This may result in expensive simulations when the viscosity is small. To address this issue, we have introduced a new class of Hybridizable Discontinuous Galerkin (HDG) finite element method for incompressible flows. We have shown, by numerical simulation, that the EDG-HDG method is up to 10 times more efficient than the HDG method”, the researcher explained about the contents presented in the context of a new version of the Seminar on Numerical Analysis and Mathematical Modeling, SANMoMA, organized by researchers from the Center for Research in Mathematical Engineering, CI²MA, and academicians from UdeC and UBB.

One of the CI²MA researchers with whom Rhebergen collaborates is the UBB Professor, Ricardo Oyarzúa. “The idea of ​​Sander's visit is to continue our joint collaboration that we started when Paulo Zúñiga went to Waterloo in the context of his doctoral thesis. From this stay, an article related to numerical methods for poro-elasticity was generated, and we wish to continue collaborating on extensions and / or problems related to that work. In turn, we are also interested in starting new projects related to numerical methods for fluid mechanics”, he explains about this stay funded by the Fondecyt 1161325 project led by him. In turn, the CI²MA researcher, Manuel Solano is a UdeC academician and, about Rhebergen's visit, he points out that “it’s been a great opportunity to strengthen our collaboration. I know Sander since 2011 when he was a postdoctoral researcher at the University of Minnesota and I was finishing my graduate studies. Both worked with Bernardo Cockburn and that is why we have common interests such as space-time HDG methods”.

Paulo Zúñiga obtained his PhD degree from UdeC a few weeks ago and currently performs a mini-postdoc at CI²MA, directed precisely by Oyarzua and Solano, who were his thesis advisorts. “I had the opportunity to meet Sander thanks to a research stay at the University of Waterloo in 2018, when I was still a PhD student. Since then, our joint collaboration aims to develop new numerical techniques for problems related to earth sciences”, he details about the collaboration with Rhebergen, whose stay at the UdeC runs between January 5 and 18.