On the Maximum Angle Condition for Linear Tetrahedral Elements

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1992 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 29, pages 513-520 (issn: 0036-1429, eissn: 1095-7170,

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Authors: Křížek, Michal;

doi: 10.1137/0729031

On the Maximum Angle Condition for Linear Tetrahedral Elements

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Abstract

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 \(p\in[1,\infty]\).

Keywords

maximum angle condition, tetrahedral elements, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Interpolation in approximation theory

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