Basis for high order divergence-free finite element spaces

A. Alonso Rodríguez (1) , Jessica Camano (2, 3) , E. de Los Santos (3) , Francesca Rapetti (4, 5)

1 UNITN - Università degli Studi di Trento = University of Trento
2 DMFA - Departamento de Matemática y Fı́sica Aplicadas [Concepcion]
3 CI²MA - Centro de Investigación en Ingeniería Matemática [Concepción]
4 UniCA - Université Côte d'Azur
5 CASTOR - Control, Analysis and Simulations for TOkamak Research

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.

Mots clés: Spanning tree; Oriented graph; Incidence matr; High order Raviart–Thomas finite elements; Divergence-free finite elements

Domaines: Analyse numérique [math.NA]

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⟩