A new H(div)-conforming p-interpolation operator in two dimensions
Alexei Bespalov and Norbert Heuer
ESAIM Math. Model. Num. Anal. 45 (2), 255-275, 2011.
In this paper we construct a new H(div)-conforming projection-based
p-interpolation operator that assumes only
Hr(K) ∩
∼H-½(div,K)-regularity
(r > 0) on the reference element K (either triangle or square).
We show that this operator is stable with respect to polynomial degrees and
satisfies the commuting diagram property. We also establish an estimate for the
interpolation error in the norm of the space
∼H-½(div,K),
which is closely related to the energy spaces for boundary integral formulations
of time-harmonic problems of electromagnetics in three dimensions.