by Matthies, G., Schieweck, F..
Series: 2006-54, Preprints
We study the properties of the reference mapping for
quadrilateral and hexahedral finite elements.
We consider multilevel adaptive grids with possibly hanging nodes
which are typically generated by adaptive refinement
starting from a regular coarse grid.
It turns out that for such grids the reference mapping
behaves -- up to a perturbation depending on the
mesh size -- like an affine mapping.
As an application, we prove optimal estimates of the interpolation
error for discontinuous mapped P_r-elements on quadrilateral and hexahedral grids.
quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes, finite element analysis