Isogeometric analysis with Powell-Sabin splines for advection-diffusion-reaction problems

This paper presents the use of Powell-Sabin splines in the context of isogeometric analysis for the numerical solution of advection-diffusion-reaction equations. Powell-Sabin splines are piecewise quadratic $C^1$ functions defined on a given triangulation with a particular macro-structure. We discuss the Galerkin discretization based on a normalized Powell-Sabin B-spline basis. We focus on the accurate detection of internal and boundary layers, and on local refinements. We apply the approach to several test problems, and we illustrate its effectiveness by a comparison with classical finite element and recent isogeometric analysis procedures.