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On Friedrichs constant and Horgan-Payne angle for LBB condition

By Monique Dauge, Christine Bernardi, Martin Costabel and Vivette Girault

Abstract

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

Topics: LBB condition, inf-sup constant, Friedrichs constant, Horgan-Payne angle, 30A10, 35Q35, [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA]
Publisher: HAL CCSD
Year: 2014
OAI identifier: oai:HAL:hal-00797642v1
Provided by: Hal-Diderot

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