Abstract: In this concluding part of a series of papers on tetrahedral polynomial extension operators, the existence of a polynomial extension operator in the Sobolev space is proven constructively. Specifically, on any tetrahedron , given a function on the boundary that is a polynomial on each face, the extension operator applied to gives a vector function whose components are polynomials of at most the same degree in the tetrahedron. The vector function is an extension in the sense that the trace of its normal component on the boundary coincides with . Furthermore, the extension operator is continuous from into . The main application of this result and the results of this series of papers is the existence of commuting projectors with good -approximation properties.
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L. Demkowicz Affiliation:
Institute of Computational Engineering and Sciences, 1 University Station, C0200, The University of Texas at Austin, Texas 78712
Email:
leszek@ices.utexas.edu
J. Gopalakrishnan Affiliation:
University of Florida, Department of Mathematics, Gainesville, Florida 32611–8105
Email:
jayg@ufl.edu
J. Schöberl Affiliation:
Technische Universität Wein, Wiedner Hauptstrasse 8-10, Wein 1040, Austria
Email:
joachim.schoeberl@tuwien.ac.at