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.
Basis for high order divergence-free finite element spaces / Alonso Rodriguez, A.; Camaño, J.; De Los Santos, E.; Rapetti, F.. - In: RESULTS IN APPLIED MATHEMATICS. - ISSN 2590-0374. - 23:(2024), pp. 10046901-10046917. [10.1016/j.rinam.2024.100469]
Basis for high order divergence-free finite element spaces
Alonso Rodriguez, A.;Rapetti, F.
2024-01-01
Abstract
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.| File | Dimensione | Formato | |
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