EXPLICIT FORMULAS FOR INTERPOLATING SPLINES OF DEGREE 5 ON THE TRIANGLE

摘要

Explicit formulas are derived for 21 Zlamal-Zenisek basis interpolating polynomials of degree 5 in each triangle of the triangulation. Their use significantly reduces 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 basis interpolating polynomials of degree 5. The formulas are also presented for interpolation operators with the use of these basis polynomials and for the integral representation of the remainder term of the approximation of differentiable functions by these operators.