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

Published online by Cambridge University Press:  02 August 2010

Alexei Bespalov and
Norbert Heuer
Alexei Bespalov
Affiliation:
Department of Mathematical Sciences, Brunel University, Uxbridge, West London UB8 3PH, UK. albespalov@yahoo.com
Norbert Heuer
Affiliation:
ANESTOC and Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile. nheuer@mat.puc.cl

Abstract

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In this paper we construct a new H(div)-conforming projection-basedp-interpolation operator that assumes only H r (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 andsatisfies the commuting diagram property. We also establish an estimate for theinterpolation 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 formulationsof time-harmonic problems of electromagnetics in three dimensions.

Keywords

p-interpolationerror estimationMaxwell's equationsboundary element method.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 2 , March 2011, pp. 255 - 275
Copyright
© EDP Sciences, SMAI, 2010

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