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Journal Articles Results in Applied Mathematics Year : 2024

Basis for high order divergence-free finite element spaces

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 fora 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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Dates and versions

hal-02429500 , version 1 (08-01-2020)
hal-02429500 , version 2 (07-02-2024)

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Cite

A. Alonso Rodríguez, Jessica Camano, E. de Los Santos, Francesca Rapetti. Basis for high order divergence-free finite element spaces. Results in Applied Mathematics, 2024, 23, pp.100469. ⟨10.1016/j.rinam.2024.100469⟩. ⟨hal-02429500v2⟩
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