# 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

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topBespalov, 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 -

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