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.

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

Domains: Numerical Analysis [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⟩