| Issue |
ESAIM: M2AN
Volume 45, Number 2, March-April 2011
|
|
|---|---|---|
| Page(s) | 255 - 275 | |
| DOI | https://doi.org/10.1051/m2an/2010039 | |
| Published online | 02 August 2010 | |
A new H(div)-conforming p-interpolation operator in two dimensions
1
Department of Mathematical Sciences, Brunel University,
Uxbridge, West London UB8 3PH, UK.
albespalov@yahoo.com
2
ANESTOC and Facultad de Matemáticas,
Pontificia Universidad Católica de Chile,
Avenida Vicuña Mackenna 4860, Santiago, Chile.
nheuer@mat.puc.cl
Received:
20
October
2009
Revised:
12
April
2010
In this paper we construct a new H(div)-conforming projection-based
p-interpolation operator that assumes only Hr(K) 
-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 -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.
Mathematics Subject Classification: 65N15 / 41A10 / 65N38
Key words: p-interpolation / error estimation / Maxwell's equations / boundary element method.
© EDP Sciences, SMAI, 2010
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