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

Alexei Bespalov; Norbert Heuer

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 45, Issue: 2, page 255-275
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bespalov, Alexei, and Heuer, Norbert. "A new H(div)-conforming p-interpolation operator in two dimensions." ESAIM: Mathematical Modelling and Numerical Analysis 45.2 (2011): 255-275. <http://eudml.org/doc/197576>.

@article{Bespalov2011,
abstract = { In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$$\{\bf \tilde 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 $\{\bf \tilde H\}$-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. },
author = {Bespalov, Alexei, Heuer, Norbert},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {p-interpolation; error estimation; Maxwell's equations; boundary element method.; -interpolation; boundary element method},
language = {eng},
month = {1},
number = {2},
pages = {255-275},
publisher = {EDP Sciences},
title = {A new H(div)-conforming p-interpolation operator in two dimensions},
url = {http://eudml.org/doc/197576},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Bespalov, Alexei
AU - Heuer, Norbert
TI - A new H(div)-conforming p-interpolation operator in two dimensions
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2011/1//
PB - EDP Sciences
VL - 45
IS - 2
SP - 255
EP - 275
AB - In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only Hr(K) $\cap$${\bf \tilde 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 ${\bf \tilde H}$-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.
LA - eng
KW - p-interpolation; error estimation; Maxwell's equations; boundary element method.; -interpolation; boundary element method
UR - http://eudml.org/doc/197576
ER -

References

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