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Extension by zero in discrete trace spaces: Inverse estimates

by R. Hiptmair and C. Jerez-Hanckes and S. Mao

(Report number 2012-33)

Abstract
We consider lowest-order $H^{-1/2}(\mathrm{div},\Gamma)$- and $H^{-1/2}(\Gamma)$-conforming boundary element spaces supported on a part of the boundary Γ 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 operatorswith 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.

Keywords:

@Techreport{HJM12_476,
  author = {R. Hiptmair and C. Jerez-Hanckes and S. Mao},
  title = {Extension by zero in discrete trace spaces: Inverse estimates},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2012-33},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2012/2012-33.pdf },
  year = {2012}
}

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