Extension by zero in discrete trace spaces: Inverse estimates
Ralf Hiptmair, Carlos Jerez-Hanckes, Shipeng Mao · Mathematics of Computation · 2015
We consider lowest-order H − 1 2 ( div Γ , Γ ) {\boldsymbol H}^{-\frac {1}{2}}(\operatorname {div}_\Gamma , \Gamma ) - and H − 1 2 ( Γ ) H^{-\frac {1}{2}}(\Gamma ) -conforming boundary element spaces supported on part of the boundary Γ \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.