A new geometric condition equivalent to the maximum angle condition for tetrahedrons

For a tetrahedron, suppose that all internal angles of faces and all dihedral angles are less than a fixed constant C that is smaller than pi. Then, it is said to satisfy the maximum angle condition with the constant C. The maximum angle condition is important in the error analysis of Lagrange interpolation on tetrahedrons. This condition ensures that we can obtain an error estimation, even on certain kinds of anisotropic tetrahedrons. In this paper, using two quantities that represent the geometry of tetrahedrons, we present an equivalent geometric condition to the maximum angle condition for tetrahedrons.

Automated summary

This paper discusses the importance of the maximum angle condition in error analysis of Lagrange interpolation on tetrahedrons, and presents an equivalent geometric condition as a replacement for the maximum angle condition.