Reference: Chap 1.1, 1.2, 1.3 from the textbook by C. Johnson

Reference: Chap 2.1, problem 1.3 from the textbook by C. Johnson, and Lecture 1 and Lecture 2 from the online lecture notes: finite element analysis from Dr. Flaherty.

Especially, see Chap 1.1 (finite element discretization of 2-point b.v.p.), 1.3 (FEM with piecewise linear functions with construction of local stiffness/mass matrices and assembly of global matrix),

and see Chap 2.1 (introduction), 2.2 (Variational formulation for general 1-D problem), 2.4 (Lagrangian polynomials as shape functions), 2.6 (interpolation errors for error estimate) from the lecture notes by Dr. Flaherty.