Extension by zero in discrete trace spaces: Inverse estimates
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- by Ralf Hiptmair, Carlos Jerez-Hanckes and Shipeng Mao PDF
- Math. Comp. 84 (2015), 2589-2615 Request permission
Abstract:
We consider lowest-order ${\boldsymbol H}^{-\frac {1}{2}}(\operatorname {div}_\Gamma , \Gamma )$- and $H^{-\frac {1}{2}}(\Gamma )$-conforming boundary element spaces supported on part of the boundary $\Gamma$ of a Lipschitz polyhedron. Assuming families of triangular meshes created by regular refinement, we prove that on these spaces the norms of the extension by zero operators with respect to (localized) trace norms increase poly-logarithmically with the mesh width. Our approach harnesses multilevel norm equivalences for boundary element spaces, inherited from stable multilevel splittings of finite element spaces.References
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Additional Information
- Ralf Hiptmair
- Affiliation: SAM, ETH Zürich, CH-8092 Zürich, Switzerland
- Email: hiptmair@sam.math.ethz.ch
- Carlos Jerez-Hanckes
- Affiliation: School of Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile
- MR Author ID: 901844
- ORCID: 0000-0001-8225-9558
- Email: cjerez@ing.puc.cl
- Shipeng Mao
- Affiliation: LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
- Email: maosp@lses.cc.ac.cn
- Received by editor(s): October 22, 2012
- Received by editor(s) in revised form: March 18, 2014
- Published electronically: April 21, 2015
- Additional Notes: The work of the second author was funded by FONDECYT 11121166 and CONICYT project Anillo ACT1118 (ANANUM)
The work of the third author was partly supported by Thales SA under contract “Preconditioned Boundary Element Methods for Electromagnetic Scattering at Dielectric Objects” and NSFC 11101414, 11101386, 11471329 - © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 2589-2615
- MSC (2010): Primary 65N12, 65N15, 65N30
- DOI: https://doi.org/10.1090/mcom/2955
- MathSciNet review: 3378840