Generative AI in FDM and FEM Numerical Methods: Prompting, Validation, and Competency-Based Learning in Engineering Education
Academic Article in Scopus
The teaching of numerical methods is essential in engineering, yet their complexity and the heterogeneity of learning curves hinder mastery, particularly when comparing the Finite Element Method (FEM) with the Finite Difference Method (FDM). To address this challenge, we integrated generative artificial intelligence (AI) as a pedagogical scaffold in a MATLABbased course with two equivalent groups: FDM (n = 28) and FEM (n=30), both under the same AI usage protocol and assessment criteria. Over five weeks, we measured accuracy (L2 error), efficiency (time), prompting quality, robustness, documentation, transfer, and AI hallucinations. Mixed-model analyses showed significant reductions in error (¿2=0.17, p<0.001) and time (¿2=0.14, p<0.001); slopes were steeper for FDM, while FEM exhibited consistent improvements under higher cognitive load. Prompting quality emerged as a predictor of performance (¿=-0.41, p<0.05). The competency radar revealed complementary profiles; heatmaps showed decreasing hallucination frequency through verification and validation; and the forest plot identified prompting (ß ¿-0.28) and systematic validation (ß ¿ - 0.22) as key factors. We conclude that generative AI, when responsibly applied, accelerates, stabilizes, and diversifies numerical learning, strengthens the instructor's role, and offers a replicable model aligned with Tec21/ABET frameworks and SDG 4: Quality Education.
