Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions
This work provides a rigorous theoretical foundation for p-interpolation error estimates in computational electromagnetics, which is important for high-order finite and boundary element methods.
The paper proves an optimal error estimate for the H(curl)-conforming projection-based p-interpolation operator on reference elements for vector fields in H^r(curl,K) with r>0, and extends the result to the H(div)-conforming setting for high-order boundary element methods for Maxwell's equations.
In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuska, p interpolation error estimates for edge finite elements of variable order in two dimensions, SIAM J. Numer. Anal., 41 (2003), pp. 1195-1208]. This result is proved on the reference element (either triangle or square) K for regular vector fields in H^r(curl,K) with arbitrary r>0. The formulation of the result in the H(div)-conforming setting, which is relevant for the analysis of high-order boundary element approximations for Maxwell's equations, is provided as well.