Stable decompositions of $hp$-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D

Karkulik, Michael; Melenk, Jens Markus; Rieder, Alexander

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 145-180.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We consider fractional Sobolev spaces H$$(Γ), θ∈[0, 1] on a 2D surface Γ. We show that functions in H$$(Γ) can be decomposed into contributions with local support in a stable way. Stability of the decomposition is inherited by piecewise polynomial subspaces. Applications include the analysis of additive Schwarz preconditioners for discretizations of the hypersingular integral operator by the p-version of the boundary element method with condition number bounds that are uniform in the polynomial degree p.

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