Non shape regular domain decompositions: an analysis using a stable decomposition in $H_0^1$

Martin J. Gander (1) , Laurence Halpern (2) , Kévin Santugini-Repiquet (3, 4)

1 Section de mathématiques [Genève]
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 IMB - Institut de Mathématiques de Bordeaux
4 MC2 - Modélisation, contrôle et calcul

In this paper, we establish the existence of a stable decomposition in the Sobolev space $H^1_0$ for domain decompositions which are not shape regular in the usual sense. In particular, we consider domain decompositions where the largest subdomain is significantly larger than the smallest subdomain. We provide an explicit upper bound for the stable decomposition that is independant of the ratio between the diameter of the largest and the smallest subdomain.

Domaines: Analyse numérique [math.NA]

Martin J. Gander, Laurence Halpern, Kévin Santugini-Repiquet. Non shape regular domain decompositions: an analysis using a stable decomposition in $H_0^1$. 2011. ⟨hal-00607043v1⟩