On the Maximum Angle Condition for Linear Tetrahedral Elements

Abstract

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 $W_p^1 (\Omega )$-norm for sufficiently smooth functions and $p \in [1,\infty ]$.