Using the finite element method to understand calculus

This paper presents a complementary, alternative teaching and learning methodology based on the use of the finite element method to illustrate mathematical models and to explore their (numerical) solutions in the context of vector calculus properties understanding. This methodology is illustrated via a set of examples focused on specific engineering problems, but its scope can also be widened to other scientific areas. The examples presented on this paper allow concluding that this approach may be an interesting way to re-think and complement the perspective usually considered in the transmission of mathematical concepts. The use of a freeware finite element method computational package, FreeFEM++ may also be an important issue to stimulate the dissemination of this phenomena modelling and comprehension approach.