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A new H(div)-conforming p-interpolation operator in 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. [email protected]
Norbert Heuer
Affiliation:
ANESTOC and Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile. [email protected]
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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.

Keywords

p-interpolationerror estimationMaxwell's equationsboundary element method.
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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