A new H(div)-conforming $p$-interpolation operator in two dimensions

Bespalov, Alexei; Heuer, Norbert

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 255-275.

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only H^r(K) $\cap$ $\widetilde{𝐇}$^-1/2(div, K)-regularity (r > 0) on the reference element (either triangle or square) K. 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 $\widetilde{𝐇}$^-1/2(div, K), which is closely related to the energy spaces for boundary integral formulations of time-harmonic problems of electromagnetics in three dimensions.

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