On Friedrichs constant and Horgan-Payne angle for LBB condition

Monique Dauge (1) , Christine Bernardi (2) , Martin Costabel (1) , Vivette Girault (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LJLL - Laboratoire Jacques-Louis Lions

In dimension 2, the Horgan-Payne angle serves to construct a lower bound for the inf-sup constant of the divergence arising in the so-called LBB condition. This lower bound is equivalent to an upper bound for the Friedrichs constant. Explicit upper bounds for the latter constant can be found using a polar parametrization of the boundary. Revisiting carefully the original paper which establishes this strategy, we found out that some proofs need clarification, and some statements, replacement.

Mots clés: LBB condition; inf-sup constant; Friedrichs constant; Horgan-Payne angle

Domaines: Analyse numérique [math.NA]

Monique Dauge, Christine Bernardi, Martin Costabel, Vivette Girault. On Friedrichs constant and Horgan-Payne angle for LBB condition. Monografías Matemáticas García de Galdeano, 39, pp.222, 2014, Twelfth International Conference Zaragoza-Pau on Mathematics, ISBN: 978-84-16028-35-1. ⟨hal-00797642⟩