Error of interpolation by sixth-degree polynomials on a triangle

The paper considers Birkhoff-type triangle-based interpolation to a two-variable function by sixth-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 estimates from below are valid for any nondegenerate triangle.