Independence of interpolation error estimates by fifth-degree polynomials on angles in a triangle

The paper considers several methods of Birkhoff-type triangle-based interpolation of two-variable function by fifth-degree polynomials. Similar estimates are automatically transferred to error estimates of related finite element method. The error estimates for the given elements depend only on the decomposition diameter, and do not depend on triangulation angles. We show that the estimates obtained are unimprovable. Unimprovability is understood in a following sense: there exists function from the given class and there exist absolute positive constants independent of triangulation such that for any nondegenerate triangle estimates from below are valid.