Finite Element Method (FEM)

The Finite Element Method is a powerful numerical method used to approximate solutions to PDEs in engineering, physics, geophysics, and structural mechanics.

🧩 Core Concepts

  • Mesh generation (triangles, tetrahedra, quads, hex)
  • Shape functions
  • Weak formulation of PDEs
  • Assembly of stiffness matrices
  • Boundary conditions (Dirichlet, Neumann)
  • Time integration schemes

🔧 Open-Source FEM Libraries

FEniCS

Automated finite element computations.
🔗 https://fenicsproject.org

deal.II

High-performance C++ FEM.
🔗 https://www.dealii.org

ElmerFEM

Multiphysics simulation.
🔗 https://github.com/ElmerCSC/elmerfem

CalculiX

Structural FEM solver.
🔗 http://www.calculix.de

MOOSE Framework

Multiphysics FE-based solver.
🔗 https://github.com/idaholab/moose

🎥 YouTube Playlists

  • Finite Element Method Tutorials
    🔗 https://www.youtube.com/results?search_query=finite+element+method

  • FEniCS Course
    🔗 https://www.youtube.com/results?search_query=fenics+tutorial

📘 Open Notes

  • MIT FEM Course Notes
    🔗 https://ocw.mit.edu/courses/finite-element-analysis

  • FEM textbook open supplements
    🔗 https://github.com/jsdillon/fem-notes