High Order Transformation Methods for Curved Finite Elements

The problem of producing basis functions for curved elementsin the finite element method is discussed. An alternative methodto the Rational Basis Functions method and the IsoparametricTransformation method is given. This method, called a High OrderTransformation method, allows any degree of approximation, likethe Rational Basis Function method, while retaining the simplicityof the Isoparametric method. A discussion of the calculationof typical integrals for the case of the three-sided elementwith two straight sides and one conic arc is given.