A new H(div)-conforming p-interpolation operator in two dimensions
This work provides a theoretical tool for high-order finite element methods in boundary integral formulations of time-harmonic electromagnetic problems, but it is an incremental mathematical construction.
The paper constructs a new H(div)-conforming projection-based p-interpolation operator that requires only H^r(K) ∩ H̃^{-1/2}(div,K)-regularity (r>0) on reference elements. The operator is stable with respect to polynomial degrees, satisfies the commuting diagram property, and yields interpolation error estimates in the H̃^{-1/2}(div,K) norm.
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.