  A simple third order compact finite element method is proposed for
one-dimensional Sturm-Liouville boundary value problems. The key idea is based
on the interpolation error estimate, which can be related to the source term.
Thus, a simple posterior error analysis or a modified basis functions based on
original piecewise linear basis function will lead to a third order accurate
solution in the $L^2$ norm, and second order in the $H^1$ or the energy norm.
Numerical examples have confirmed our analysis.
