A method of Hermite interpolation by polynomials of the third degree on a triangle

As a rule, in constructing triangular finite elements of Hermite or Birkhoff type, the denominators of interpolation error bounds contain the sine of the minimum angle in the triangle. This leads to the necessity to impose some restrictions on the triangulation of the domain. Excluding the paper by Yu. N. Subbotin published in the present issue, the author does not know any description of the cases where the minimum angle is absent in the estimates of all derivatives up to order $n$ inclusive when a function is interpolated by Hermite or Birkhoff's polynomial of degree $n$. In this paper, a new method of Hermite interpolation of a function in two variables on a triangle by polynomials of degree 3 is suggested. For the proposed method, the sine of the minimum angle is absent in the denominators of error bounds for any derivatives of the function up to the third order, which makes it possible to weaken our requirements on the triangulation.