Numerical integration of rational bubble functions with multiple singularities

Abstract

We derive an effective quadrature scheme via a partitioned Duffy transformation for a class of Zienkiewicz-like rational bubble functions proposed by J. Guzmán and M. Neilan. This includes a detailed construction of the new quadrature scheme, followed by a proof of exponential error convergence. Briefly discussed is the functions application to the finite element method when used to solve Stokes flow and elasticity problems. Numerical experiments which support the theoretical results are also provided.