A new H(div)-conforming p-interpolation operator in two dimensions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 2, p. 255-275

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) 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 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.

DOI : https://doi.org/10.1051/m2an/2010039
Classification:  65N15,  41A10,  65N38
Keywords: p-interpolation, error estimation, maxwell's equations, boundary element method
@article{M2AN_2011__45_2_255_0,
     author = {Bespalov, Alexei and Heuer, Norbert},
     title = {A new H(div)-conforming $p$-interpolation operator in two dimensions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {2},
     year = {2011},
     pages = {255-275},
     doi = {10.1051/m2an/2010039},
     zbl = {1277.78031},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2011__45_2_255_0}
}
Bespalov, Alexei; Heuer, Norbert. A new H(div)-conforming $p$-interpolation operator in two dimensions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 2, pp. 255-275. doi : 10.1051/m2an/2010039. http://www.numdam.org/item/M2AN_2011__45_2_255_0/

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