Abstract.Explicit formulas are given for 21 Zlamal–Zhenishek base interpolation polynomials of 5th degree in each triangle of the triangulation. Their use can significantly reduce the number of arithmetic operations in the FEM, because otherwise 21 systems with 21 unknowns should be solved in each triangle to find all the 21 coefficients of each of the base interpolation polynomials of 5th degree. The formulas are also presented for interpolation operators with the use of these base polynomials and for the integral representation of the remainder term of the approximation of differentiable functions by these operators.

Keywords: Zlamal–Zenisek interpolating polynomials of degree 5 on triangle, explicit formulas for basis polynomials of degree 5, integral representation of remainder term, Subbotin error estimate, interpolation operator.