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Publications in Scientific Journals:

M. Karkulik, J. Melenk, A. Rieder:
"Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D";
ESAIM: Mathematical Modelling and Numerical Analysis, 54 (2020), 145 - 180.

English abstract:
We consider fractional Sobolev spaces H^(\theta)(\Gamma), \theta \in [0, 1] on a 2D surface Γ. We show that functions in H^(\theta(\Gamma) 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.

Keywords:
hp-FEM, hp-BEM, preconditioning, stable decomposition

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Created from the Publication Database of the Vienna University of Technology.