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SUMMARYThe standard adaptive edge finite element method (AEFEM), using first/second family Nédélec edge elements with any order, for the three-dimensional H(curl)-elliptic problems with variable coefficients is shown to be convergent for the sum of the energy error and the scaled error estimator. The special treatment of the data oscillation and the interior node property are removed from the proof. Numerical experiments indicate that the adaptive meshes and the associated numerical complexity are quasi-optimal.

a b s t r a c tA Fortin operator is constructed to verify the discrete inf-sup condition for the lowest order Taylor-Hood element and its variant in two dimensions. The approach is closely related to the recent work by Mardal et al. (2013). That is based on the isomorphism of the tangential edge bubble function space to a subspace of the lowest order edge element space. A more precise characterization of this subspace and a numerical quadrature are introduced to simplify the analysis and remove the mesh restriction. The constructed Fortin operator is stable in both H 1 and L 2 norm for general shape regular triangulations.