FEM Mesh Convergence of a Cantilever Beam Using COMSOL Multiphysics for Vocational Engineering Education

Abstract

Finite element method (FEM) accuracy is influenced by mesh discretization, whereas excessively fine meshes can impose disproportionate computational costs. This study analyzes mesh convergence in a rectangular cantilever-beam model and identifies the mesh level that provides the best balance between accuracy and efficiency in COMSOL Multiphysics as an instructional case for vocational engineering education. A numerical experiment was performed using five physics-controlled mesh levels: Coarse, Normal, Fine, Finer, and Extra Fine. The three-dimensional domain was discretized using an unstructured free-tetrahedral mesh with quadratic displacement interpolation. The observed parameters were element count, degrees of freedom (DOF), maximum displacement, maximum stress, relative error between successive mesh levels, and computation time. Maximum displacement increased from 0.432 mm with the Coarse mesh to 0.470 mm with the Extra Fine mesh, while maximum stress increased from 112.45 to 132.05 MPa. At the Finer level, the relative errors in displacement and stress decreased to 0.64% and 1.26%, respectively, with a computation time of 8.6 min. Refinement to Extra Fine changed displacement by only 0.21% and stress by 0.48%, but increased computation time by 148.84%. Based on an error threshold below 2% and resource efficiency, the Finer mesh was selected as the optimum configuration. The results also demonstrate how convergence metrics and stress-contour comparisons can train students to distinguish visually plausible outputs from numerically verified solutions before FEM results are used for engineering evaluation.