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2006-54

On the Reference Mapping for

by Matthies, G., Schieweck, F..


Series: 2006-54, Preprints

MSC:
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
65N15 Error bounds
65N50 Mesh generation and refinement

Abstract:
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.

Keywords:
quadrilateral and hexahedral finite elements, multilevel adaptive grids, hanging nodes, finite element analysis