Abstract
In this paper we prove an optimal error estimate for the ${\bf H}({\rm curl})$-conforming projection-based p-interpolation operator introduced in [L. Demkowicz and I. Babuška, SIAM J. Numer. Anal., 41 (2003), pp. 1195–1208]. This result is proved on the reference element (either triangle or square) K for regular vector fields in ${\bf H}^r({\rm curl},K)$ with arbitrary $r >0$. The formulation of the result in the ${\bf H}({\rm div})$-conforming setting, which is relevant for the analysis of high-order boundary element approximations for Maxwell's equations, is provided as well.
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