OPTIMAL ERROR ESTIMATION FOR H(curl)-CONFORMING p-INTERPOLATION IN TWO DIMENSIONS

摘要

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, 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.