2025/02/05 by Vı́ctor Domínguez, Dominguez, Victor, Alejandro Espinal Duque +1
Engineering · Energy · #Mechanical and Thermal Properties Analysis #Mechanical Engineering and Vibrations Research #Mechanical Systems and Engineering
paper · pdf · doi:10.48550/arxiv.2502.03248
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM provides significant educational value, provides a deeper understanding of the method, and enables the development of custom solutions tailored to specialized applications or integration with other solvers. This work introduces a 3D ℙm-element FEM implementation in MATLAB/Octave that is designed to balance educational clarity with computational efficiency. A key feature is its integration with GMSH, an open-source 3D mesh generator with CAD capabilities that streamlines mesh generation for complex geometries. By leveraging GMSH data structures, we provide a seamless connection between geometric modeling and numerical simulation. The implementation focuses on solving the general convection-diffusion-advection equation and serves as a flexible foundation for addressing advanced problems, including elasticity, mixed formulations, and integration with other numerical methods.