Isogeometric analysis in advection–diffusion problems: Tension splines approximation

We present a novel approach, within the new paradigm of isogeometric analysis introduced by Hughes et al. (2005) [6], to deal with advection dominated advection–diffusion problems. The key ingredient is the use of Galerkin approximating spaces of functions with high smoothness, as in IgA based on classical B-splines, but particularly well suited to describe sharp layers involving very strong gradients.