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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.03248 |
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| _version_ | 1866912221308649472 |
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| author | Dominguez, Victor Duque, Alejandro |
| author_facet | Dominguez, Victor Duque, Alejandro |
| contents | 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 $\mathbb{P}_m$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Practical Introduction to FEM with GMSH: A MATLAB/Octave Perspective Dominguez, Victor Duque, Alejandro Numerical Analysis 65N30 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 $\mathbb{P}_m$-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. |
| title | Practical Introduction to FEM with GMSH: A MATLAB/Octave Perspective |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2502.03248 |