4.2 Finite Element Analysis for a 1D Problem

In general, the steps involved in the FEM analysis of a typical problem can be summarized as follows [116]:

1. Introduce the mathematical problem defined in a domain;
2. Discretize the domain into finite elements;
3. Derive the element equations over each finite element in the domain;
4. Assemble the element equations to obtain equations for the entire problem;
5. Impose boundary conditions of the problem;
6. Solve the global system of equations.

A step-by-step FEM procedure for the formulation and the solution of a boundary value problem in 1D domain subject to specified boundary conditions is shown in the following subsections.