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Keywords:
simplicial element; maximum angle condition; interpolation error; higher-dimensional problem; $d$-dimensional sine; semiregular family of simplicial partitions
simplicial element; maximum angle condition; interpolation error; higher-dimensional problem; $d$-dimensional sine; semiregular family of simplicial partitions
Summary:
The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ${\mathbb R}^d$ that degenerate in some way.
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