Some historical remarks on the positivity of boundary integral operators

Martin Costabel (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Variational arguments go back a long time in the history of boundary integral equations. Energy methods have shown up very early, then virtually disappeared from the common knowledge and eventually resurfaced in the context of boundary element methods. We focus on some not so well known parts of classical works by well known classical authors and describe the relation of their ideas to modern variational principles in boundary element methods.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Histoire et perspectives sur les mathématiques [math.HO]

Martin Costabel. Some historical remarks on the positivity of boundary integral operators. Schanz, Martin; Steinbach, Olaf. Boundary Element Analysis - Mathematical Aspects and Applications, Springer, pp.1-27, 2007, Series: Lecture Notes in Applied and Computational Mechanics Vol. 29. ⟨hal-00022885⟩