Results in Applied Mathematics (Aug 2024)

Basis for high order divergence-free finite element spaces

  • A. Alonso Rodríguez,
  • J. Camaño,
  • E. De Los Santos,
  • F. Rapetti

Journal volume & issue
Vol. 23
p. 100469

Abstract

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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.

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