Learning the Finite Element Method in 1D

We solve a diffusion-reaction equation, with a source term, in 1D.

In Step-0, I provide a basic introduction.

• Some FEM concepts, such as the assembly of the global matrix per element, the reference element, ... are not discussed at first.
• At the end of the Jupyter Notebook, I finally do the global assembly by looping over elements.

In Step-1, we introduce more advanced concepts:

• the reference element
• computing the local matrices using a numerical quadrature
• material properties will now be piece-wise constant, that is, the regions of the geometry (where material properties live) and the spatial mesh are two distinct concepts.

In Step-2, we code a class for the MESH

• we handle material property layout
• mesh generation, including the use non-uniform meshes

In Step-3, we introduce other boundary conditions and code a class for the Finite-Element Method