Abstract
We propose a Scott-Zhang type finite element interpolation operator of first order for the approximation of H1-functions by means of continuous piecewise mapped bilinear or trilinear polynomials. The novelty of the proposed interpolation operator is that it is defined for general non-affine equivalent quadrilateral and hexahedral elements and so-called 1-irregular meshes with hanging nodes. We prove optimal local approximation properties of this interpolation operator for functions in H1. As necessary ingredients we provide a definition of a hanging node and a rigorous analysis of the issue of constrained approximation which cover both the two- and three-dimensional case in a unified fashion.
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