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On Synge-type angle condition for \(d\)-simplices. (English) Zbl 1424.65220
Summary: The maximum angle condition of J. L. Synge [The hypercircle in mathematical physics. A method for the approximate solution of boundary value problems. Cambridge: Cambridge University Press (1957; Zbl 0079.13802)] 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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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