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On the maximum angle condition for linear tetrahedral elements. (English) Zbl 0755.41003

Summary: Synge’s maximum angle condition for triangular elements is generalized to tetrahedral elements. For the generalized condition, it is proved that tetrahedra may degenerate in a certain way and the error of the standard linear interpolation remains \(O(h)\) in the \(W^ 1_ p(\Omega)\)-norm for sufficiently smooth functions and \(p\in[1,\infty]\).

MSC:

41A05 Interpolation in approximation theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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