Abstract
A third-order nonstandard finite element method is proposed for one-dimensional elliptic problems. A new local finite element approximation is constructed on every element using local linear basis functions with a correction term, which is exact for quadratic functions. Combining this local finite element approximation and Choosing linear finite element space as a test space, a new finite element method is developed. Numerical experiments show that this nonstandard finite element method have three order accuracy while the degree of freedom is the same as the traditional linear finite element method.