An extension theorem for polynomials on triangles
Norbert Heuer and Florian Leydecker
Calcolo 45 (2), 69-85, 2008.
We present an extension theorem for polynomial functions that proves
a quasi-optimal bound for a lifting from L2 on edges onto a fractional
order Sobolev space on triangles. The extension is such that it can be
further extended continuously by zero within the trace space of H1.
Such an extension result is critical for the analysis of non-overlapping
domain decomposition techniques applied to the p- and hp-versions
of the finite and boundary element methods for elliptic problems of
second order in three dimensions.