First Instances of Univariate and Tensor‐product Multivariate Generalized Expo‐Rational Finite Elements

摘要

We consider a construction of finite elements (FE) which is, in some sense, dual to the construction of generalized expo‐rational B‐splines (GERBS)[1, 2]. The main result is the introduction of univariate and multivariate tensor‐product GERBS‐based FE which exhibit Hermite interpolatory properties. The derivation of these results is based on the theory of C~∞‐smooth expo‐rational B‐splines (ERBS) and C~k‐smooth, k? = ?0,1,2,... piecewise polynomial GERBS called Euler Beta‐function B‐splines. We provide visualization of the approximations of some model curves and surfaces using the new FE, as well as of the size and distribution of the error of these approximations.