Geodesic
On a~multidimensional analogue of the Schwarz example
Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 681-687

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We use the Delaunay triangulation to construct a series of examples showing that in the multidimensional case, in contrast to the two-dimensional case, the approximation property for derivatives fails to hold for piecewise-linear approximations of a smooth function. These examples are closely related to the classical Schwarz example concerning piecewise-linear approximations of the lateral surface of a right circular cylinder.
Keywords: classical Schwarz example
Mots-clés : Delaunay triangulation. 
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     author = {V. A. Klyachin},
     title = {On a~multidimensional analogue of the {Schwarz} example},
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V. A. Klyachin. On a~multidimensional analogue of the Schwarz example. Izvestiya. Mathematics , Tome 76 (2012) no. 4, pp. 681-687. http://geodesic.mathdoc.fr/item/IM2_2012_76_4_a2/