Alejandro Hopper and Gonzalo Benavides are students of Mathematical Civil Engineering, MCI, at Universidad de Concepción, UdeC. While the first one is in the fifth year of the degree, the second one is already developing his degree memory directed by Leonardo Figueroa, an academician from the Department of Mathematical Engineering of the Faculty of Physical and Mathematical Sciences of the UdeC, and a member of the Center for Research in Mathematical Engineering, CI²MA.

Alejandro and Gonzalo have attended some courses together. In particular, two of them (Functional Analysis and Mixed Finite Elements Methods) were taught by the Director of CI²MA, Gabriel Gatica, who, during the second one, invited them to collaborate on one of the research topics in which he has been working with thesis students and other researchers. This aiming to replace a contest note. The interest of both students in knowing more details about the research work and even to be actively involved in them, led them to immediately accept the proposal, so that with the support of Sergio Caucao (by then, CI²MA postdoc, and today performing another postdoctorate in the U. of Pittsburgh, USA), and Gatica himself, were given to the task of solving a mathematical problem originated in an paper already published, facing it from a new theoretical and computational perspective.

“In my lessons, I usually tell my students on some of the research topics in which I have been involved in recent years with various collaborators. At some point, I got the idea of offering them to replace the second evaluation with a work on one of those topics. In addition to the change in the way of evaluating them, the possibility of effectively doing research and, eventually, writing an paper later on, Alejandro and Gonzalo found it very interesting, so they accepted the offer with great enthusiasm. Certainly, I took care of giving them a problem for which a way to approach it could be visualized in advance, so that what I assigned them finally came to be a significant improvement of something that I had previously developed with Mario Álvarez in his PhD thesis”, Gatica details .

“In their paper, they addressed this problem in a way that generated certain advantages in obtaining the approximate solution, and the challenge that Professor Gatica presented to us was that we should think over the analysis trying to obtain a method that were even numerically less expensive, using other more complex theoretical tools”, details Gonzalo -original from Talca and currently living in Hualpén- and adds that “I appreciate the opportunity that the Professor gave us to show us what research is”. “At first it was hard. That allowed us to have a much closer idea to what doing research means”, Alejandro says. “Sergio Caucao helped us a lot too, guiding us, especially in the computational work that we had to develop. We got to know tools that we did not know, mathematical results that, although they were not part of the course, did end up being a good feedback” explains the native from Lota where he currently lives. “Since I was little, I always had mathematical skills and when choosing a career I was undecided between the Bachelor's Degree and Engineering and what helped me deciding was the curricular plan, seeing that the courses were more demanding in Engineering, especially in applied mathematics”, Alejandro details about his professional option. “We have had excellent teachers. Professor Gatica, for example, has taught us far beyond what the courses program details, because he also explains the work he has done as a researcher, ”he details.

In the same way, Gonzalo specifies that he chose this career because “I care that mathematics can be applied in real physical phenomena. Perhaps, not in the short term, but in the future, the work one is doing can help to model a real problem”. Beyond the taught contents, Gonzalo also highlights that, during this research experience, carried out within the context of a course, they were able to develop new skills that are not acquired in the normal classes’ activities. “You know that the tasks that the teachers propose can be solved, everything is planned so that one achieves the objective. This is different, because you are trying to expand the frontiers of knowledge, then anything can come out”. Alejandro emphasizes the point and states “nothing is guaranteed. In fact, we started addressing the problem in a certain way and we had to change some aspects in the process, for example regarding the boundary conditions. We tried to look for different alternatives, but the theoretical tools did not exist yet”.

The work developed by the two academicians and the two undergraduate students have given rise to the pre-publication of a paper, co-authored by the four: A new mixed-primal finite element method for a coupled flow-transport problem, in which it is presented and analyzes a new finite element method for a transport problem in fluid mechanics. “Without a doubt, this is an important experience for them. I think it could be very relevant, especially given the formative stage they are currently in”, Gatica explains. Gonzalo details that he foresees himself in research area and that, parallel to the development of his thesis work, he is looking for opportunities to continue studying on this research area. “I see myself researching, I would like to work as a research academician” he says. In this regard, Alejandro explains “before living this experience, research and teaching were some of my professional objectives. And this stimulates me even more. I was able to know a little better what the area was like and that strengthened my interest. In addition to getting so many tools that will allow me to conduct other studies or to collaborate with someone else”, he emphasizes.