Isogeometric collocation methods with generalized B-splines

We introduce isogeometric collocation methods based on generalized B‐splines and we analyze their performance through numerical examples for univariate and multivariate scalar‐ and vector‐valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resulting method combines the favorable properties of isogeometric collocation and the geometrical and analytical problem‐oriented advantages of generalized B‐splines.