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.

翻译：为一维的Sturm-Liouville边界值问题提议了一个简单的第三顺序紧凑有限要素方法。关键概念基于内插误差估计,该估计可能与源词有关。因此,一个简单的后置误差分析或根据原始的笔边线性函数修改的基础函数,将导致在$L__2美元规范中出现一个第三顺序准确的解决方案,第二个顺序为$H__1美元或能源规范。数字实例证实了我们的分析。