FEM Companion Notebooks
These notebooks accompany the Introduction to the Finite Element Method lecture notes. Each one is a hands-on exercise that lets you work through the key ideas symbolically and numerically using the symbolic_fem_workbench package.
Related resources:
- Lecture Notes — each chapter links to its companion notebooks at the top, and a single-file PDF download of the whole book is available.
- Package Documentation — API reference for the
symbolic_fem_workbenchpackage used below. - Source Repository — issues and edit-on-GitHub links on every notebook.
| # | Notebook | Topic |
|---|---|---|
| 1 | Strong to Weak Form | Weighted residuals, integration by parts |
| 2 | Galerkin Discretization | Element matrices from weak form |
| 3 | 1D Element Stiffness | Symbolic → numerical assembly |
| 4 | Exact vs. Gauss Integration | Quadrature rules |
| 5 | Reference Element Gallery | Shape functions in 1D/2D/3D |
| 6 | 2D Triangle Poisson | Gradient pullback, local tensors |
| 7 | Manual 2D Assembly | Global stiffness from local elements |
| 8 | Boundary Conditions 1D | Dirichlet & Neumann in 1D |
| 9 | Boundary Conditions 2D | Neumann edges, Dirichlet lifting |
| 10 | 2D Elasticity | P1 triangles, stress/strain |
| 11 | 3D Elasticity | P1 tetrahedra |
| 12 | Code Generation & Widgets | Interactive exploration |
| 13 | Time-Dependent FEM | Mass matrix, time stepping |
| 14 | Error Analysis | Convergence rates |