A Computational Interactive Approach to Support the Teaching–Learning Process of the Finite Element Method

Abstract

The teaching-learning process of subjects with sophisticated mathematical content such as the Finite Element Method (FEM) involves challenges such as a high degree of conceptual abstraction, complicated translations into computer languages, and signif icant challenges in visualizing physical phenomena and their discrete representations, among others. It is therefore appropriate to rely on innovative teaching strategies that promote students’ understanding and meaningful assimilation of the content. In this work, we propose an interactive approach through a computational tool to support this process, with an emphasis on support to facilitate conceptual understanding while inviting active participation through continuous feedback during the study. This approach allows for parameter manipulation, as well as visualization and simulation of results, thus facilitating the dynamic discovery of FEM principles. The FEM is chosen as a case study because it is a place where important theoretical and practical aspects converge, and its implementation in home programs leads to challenges of moderate difficulty. The mathematical theory underlying the FEM is briefly described, along with the methodology used for its development and the architecture of the system. As a result, the benefits this proposal offers for the study of complex content are evident, both in the classroom, where teachers can offer varied examples to their students following a syllabus, and outside of class, as it allows students to explore ideas at their own pace and discover patterns that might have been hidden in a first approach to the topics. It also provides an adaptable reference to guide individual implementations, which are often required in courses such as those on the FEM.