Extension by zero in discrete trace spaces: Inverse estimates

Ralf Hiptmair, Carlos Jerez-Hanckes, Shipeng Mao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider lowest-order H -1/2 (div Γ, Γ)- and H -1/2 (Γ)-conforming boundary element spaces supported on 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 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.

Original languageEnglish
Pages (from-to)2589-2615
Number of pages27
JournalMathematics of Computation
Volume84
Issue number296
DOIs
StatePublished - 2015
Externally publishedYes

Keywords

  • Boundary finite element spaces
  • Inverse estimates
  • Multilevel norm equivalences

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