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Basis for high order divergence-free finite element spaces
Dra. Camaño-Valenzuela, Jessika
Facultad de Ingeniería
Alonso-Rodríguez, A.
De Los Santos, E.
Rapetti, F.
Elsevier
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.
Tree-cotree
DeRham diagram
High-order finite elements