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

Details A new H(div)-conforming p-interpolation operator in two dimensions A new H(div)-conforming p-interpolation operator in two dimensions

2009-10-20

arxiv.org/abs/0910.3891v1

Mathematics

Numerical Analysis

26 pages

Scientific paper

In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only $H^r(K) \cap \tilde H^{-1/2}(div,K)$-regularity (r > 0) on the reference element K (either triangle or square). 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 $\tilde H^{-1/2}(div,K)$, which is closely related to the energy spaces for boundary integral formulations of time-harmonic problems of electromagnetics in three dimensions.

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