Finite Element Method for Solving 1-D Boundary Value Problem

Finite element method (FEM) is a numerical method for solving boundary value problem. The purpose of FEM is to solve partial differential equation (PDE) with specific boundary conditions. It is firstly applied in solid mechanics, and later extended to fluid mechanics, heat transfer, electromagnetism and so on, which is involved to the physics field problems. This paper will discuss applying three different methods to obtain the corresponding approximate solutions from a solvable differential equation. It is proved that the result from Galerkin method is the closest to the exact solution by comparing with the exact solution.