Multivariate weak spline function space (Q1612373)

Weak splines are defined similarly to the classical, differentiable polynomial splines, except that their required smoothness (i.e. usually at least continuity) is defined over discrete point sets rather than over domains. Therefore they generate larger spaces that the ones defined by the usual polynomial splines. In this paper, certain properties of spaces of weak splines are discussed which are classical in the polynomial spline case. Among others, these are the dimension of spline spaces, B-splines and splines on type-1 triangulations.