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

Michael Karkulik, Jens Markus Melenk, Alexander Rieder

We consider fractional Sobolev spaces $H^{\theta }(\Gamma )$, $\theta \in [0,1]$, on a 2D surface $\Gamma$. We show that functions in $H^{\theta }(\Gamma )$ can be decomposed into contributions with local support in a s…