Improving the selection of interior points for one-dimensional finite element methods

A new strategy to improve the selection of interior points inside an element of finite element methods is proposed. The novelty is to use the element boundary information in selecting the internal points. The new strategy is compared to the classical strategy in several examples and the main benefits are qualitatively and quantitatively explained.

► Improve the selection of interior points for a better polynomial interpolation.
► Boundary information of each finite element is exploited in the selection.
► A general benefit is obtained for finite element methods.
► Polynomial and interpolated function gap is significantly reduced.