On the numerical performance of FEM based on piecewise rational smooth resolutions of unity on triangulations

This work is a comparative study of a number of recently introduced finite element methods based on generalized expo-rational B-splines [7, 9]. In [12] a new construction of piecewise-rational C^m-smooth resolution of unity on triangulated domains in $R2$⁠, m = 1,2, …, has been introduced. The present work is a first study of the potential for applications of this new construction in the numerical analysis of boundary-value problems for PDEs. It also represents a continuation and complement of certain aspects of the study in [23] which was conducted before the introduction of the new construction in [12] and the introduction of the logistic expo-rational B-spline in [10].