Extension of Dasgupta’s Technique for Higher Degree Approximation

Abstract

In the present paper, rational wedge functions for degree two approximation have been computed over a pentagonal discretization of the domain, by using an analytic approach which is an extension of Dasgupta’s approach for linear approximation. This technique allows to avoid the computation of the exterior intersection points of the elements, which was a key component of the technique initiated by Wachspress. The necessary condition for the existence of the denominator function was established by Wachspress whereas our assertion, induced by the technique of Dasgupta, assures the sufficiency of the existence. Considering the adjoint (denominator) functions for linear approximation obtained by Dasgupta, invariance of the adjoint for degree two approximation is established. In other words, the method proposed by Dasgupta for the construction ofWachspress coordinates for linear approximation is extended to obtain the coordinates for quadratic approximation. The assertions have been supported by considering some illustrative examples.