In this paper, we focus on the high order Lagrange finite element in two- and three-dimension spaces. We use an essential theorem about anisotropic interpotation to check the anisotropy of the elements, which is easer to be operated or applied than Apel's. Quadrilateral, trianglar, hexaheral, tetrahedral elements are considered respectively.And anisotropic error estimates of the interpolation error in the energy norm and the L~2-norm are given.
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