Using Artificial Intelligence in Numerical Methods Courses: Risks and Opportunities

Abstract

In many engineering courses, students use Finite Element Method (FEM) software without knowing its fundamentals, assuming results as valid even when they lack physical meaning. Similarly, Large Language Models (LLM) such as GPT or Deepseek allow code generation for Computational Fluid Dynamics (CFD), but without ensuring understanding of the algorithmic logic or mathematical foundations. While these tools facilitate obtaining basic code fragments, their uncritical use increases the risk of modeling and implementation errors. This work proposes a pedagogical approach in which students produce, translate, and optimize code with LLM support, based on traditional bibliographic references. Line-by-line review favors understanding of program structure, implementation logic, and criteria for validating results. The methodology was evaluated in two editions of the CFD course for the Mechanical Engineering degree. Students showed a stronger understanding of numerical methods compared to previous cohorts, and in final interviews they expressed a more critical view regarding the use of Artificial Intelligence tools in learning