A new H(div)-conforming p-interpolation operator in two dimensions
Department of Mathematical Sciences, Brunel University,
Uxbridge, West London UB8 3PH, UK.
2 ANESTOC and Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile. email@example.com
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