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

Abstract

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.

26 pages

References in corpus (4)

• Discrete compactness for the p-version of discrete differential forms
• Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions
• Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces
• The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis