Assembly
The assembly algorithm has been credited to many different people and has numerous forms. The heart of the algorithm is always the same, input the weak form of the PDE, the domain representation (usually a mesh), and an approximating finite element space, output a matrix equation, or equivalent operator. Usually the matrix equation is handed to your linear algebra routines, but matrix-free assembly will apply the linear algebra routines in the assembly process. See basic assembly for the basic routine.
