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 \(\mathbb{P}_r\) -elements on quadrilateral and hexahedral grids.
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Matthies, G., Schieweck, F. On the reference mapping for quadrilateral and hexahedral finite elements on multilevel adaptive grids. Computing 80, 95–119 (2007). https://doi.org/10.1007/s00607-007-0228-0
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DOI: https://doi.org/10.1007/s00607-007-0228-0