Basis for high order divergence-free finite element spaces - A. Alonso Rodríguez; J. Camaño; E. De Los Santos; F. Rapetti (Results in Applied Mathematics, 2024)
A method classically used in the lower polynomial degree for the construction of a finite element basis of the space of divergence-free functions is here extended to any polynomial degree for a bounded domain without topological restrictions. The method uses graphs associated with two differential operators: the gradient and the divergence, and selects the basis using a spanning tree of the first graph. It can be applied for the two main families of degrees of freedom, weights and moments, used to express finite element differential forms.