Alejandra Barrios, student of Mathematical Civil Engineering of the Universidad de Concepción, has been visiting Brown University (Rhode Island, United States) since March. This research stay has been organized by her director of undergraduate thesis Manuel Solano, faculty of the Department of Mathematical Engineering (DIM) and researcher at the Center for Research in Mathematical Engineering, CI²MA.

During her visit at Brown U., from March 2 to May 25, Alejandra is collaborating with Johnny Guzmán, faculty of the Division of Applied Mathematics of Brown University and Javier Sayas, faculty of the Department of Mathematical Sciences of the University of Delaware who is currently visiting Brown. “The main objective is to finish my undergraduate thesis that consists of proposing and analyzing a hybridizable discontinuous Galerkin method for the biharmonic problem on polygonal domains. The approximation of one of the variables in the method that we proposed is not optimal, and that is why part of my stay here consists of modifying the method in order to make that approximation optimal”, the student details from the USA and explains that one of her permanent motivations is “to learn new things and get ideas to work in the future, for example, to extend the method to curved domains, to develop an a posteriori error estimator or to study the Reissner-Mindlin plate model, from which the biharmonic problem can be obtained”. In addition, Alejandra emphasizes, in more general terms, having the chance to live “the experience to see how the academic world works in the United States and to interact with researchers like Javier and Johnny”.

In the same direction, Manuel Solano explains that, in the Mathematical Civil Engineering program, “We try to send our students abroad to do research in collaboration with international faculties. Johnny Guzmán is an expert in what Alejandra is working on and that is why I thought he is the right person for her to visit. Now, Alejandra was lucky because Javier Sayas is currently a visiting professor at Brown, so she has taken advantage of working with both of them”, the faculty explains about the stay that was funded by Fondecyt Project 1160320 and Basal Project PFB 03. Regarding the contacts that made this stay possible, Solano explains that the collaboration of researchers from CI²MA with both, Guzmán and Sayas, has been constant since long time ago and that the director of the Center, Gabriel Gatica, dedicates an important part of his efforts to promote the relevance of this kind of interactions. “He (Gatica) has previously sent his students to work with both Javier and Johnny. Even his ex-students have graduated from PhD programs or are currently pursuing PhD degrees at the universities of Brown and Delaware. From my side, I met Javier and Johnny at the U. of Minnesota. There, I was a PhD student, Johnny a postdoc and Javier a visiting professor. The three of us collaborating with Bernardo Cockburn. Then Johnny was hired as a faculty at Brown, Javier also as a faculty in Delaware and I as a postdoc in Delaware”, the researcher explains.

In addition to the research work that Alejandra is doing, her stay at Brown U. has allowed her to “take the opportunity to attend to English tutorials at the International House of Rhode Island, a multicultural non-profit organization that offers, in addition to the tutorials, instances that bring together people of different nationalities”. On the other hand, Alejandra mentioned that during her stay, the faculty Mark Ainsworth was offering a course on High Order Finite Element Method, so, she explains that “I took the advantage of attending to his classes. I have also attended to the course Applied Partial Equations in which Ernesto Cáceres is the teaching assistant”. It should be mentioned that Ernesto Cáceres is a Mathematical Civil Engineer from UdeC, who is currently pursuing a Doctorate in Applied Mathematics at Brown.