If we use only two Hermite shape functions for solutions and do not use other two for derivatives of the solution, this graph shows that the approximate solution is bad even though the solution is continuously differentiable. However, if we use all four Hermite shape functions, this graph shows that Hermite FE approximation is good. In fact, it is exact. Furthermore, this graph shows that Hermite FE approximation is much better than this linear FE approximation with the same mesh [-1, 0.5, 0, 0.5, 1].
On the other hand, if the solution is not continuously differentiable, this graph shows that Hermite FE approximation is bad even though we use all four Hermite shape functions. In fact, It is worse than the linear FE approximation with the same mesh [-1, 0.5, 0, 0.5, 1].
