Polynomial extensions of compatible polynomial traces in three dimensions
The author describes polynomial extensions of compatible polynomial traces on the boundary \(\partial \Omega\) (or on some parts of the boundary) of the cube \(\Omega = (0,1)^3\) to its interior, and shows stability estimates with respect to the corresponding Sobolev space scales. These results are not only of pure theoretical interest but play an important role in the construction of domain decomposition preconditioners as well as in estimating the relative condition number of domain decomposition preconditioners for the so-called \(p\) finite element methods and for spectral finite element methods.
scientific article; zbMATH DE number 764278
scientific article