Evaluation of 'specia' finite elements with non-conventional Gaussian quadratures

Finite elements with ‘Special’ basis functions have been proposed to develop better approximations for problems where the behaviour is known to be non‐polynomial. This paper discusses extension of Gaussian quadrature integration procedures of non‐conventional form to the evaluation of the finite element matrices for ‘Special’ elements. Algorithms for general ‘Special’ elements are discussed. The techniques are applied to ‘Special’ one‐ and two‐dimensional elements for spherically symmetric potential flow. The accuracy of the new ‘Special’ element is shown to be superior to linear and quadratic elements for spherically symmetric potential flow problems.