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 C1 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 …

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 C1 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 …