Finite Element from Scratch in Python

Introduction

The best way to learn FEM is to implement it yourself. This tutorial depends on no existing framework - starting from triangular elements, it builds a 2D linear-elastic solver in pure NumPy/SciPy, covering the full pipeline from meshing to post-processing. For engineers and students who want to deeply understand FEM internals.

Path

Chapter 1: Triangular elements & shape functions (2-3 days)

• Understand FEM core: from weak form to element matrix
• Implement shape functions and their Jacobians

Chapter 2: Stiffness assembly (2-3 days)

• Global stiffness assembly logic
• Gaussian integration; sparse COO assembly

Chapter 3: Boundary conditions & solve (1-2 days)

• Dirichlet/Neumann handling
• SciPy sparse solver; stress recovery

Chapter 4: Meshing & post-processing (1-2 days)

• Delaunay triangulation; matplotlib contours

Who it's for

• Mech/civil/aero students who know FEM formulas but want to verify by hand
• Programmers wanting first-principles FEM, not just software operation
• A foundation before learning FEniCS / Abaqus