Abstract:In this paper we present a unified framework for constructing spectrally equivalent low-orderrefined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div), and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart-Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spe… Show more
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