O. Davydov, Stable local bases for multivariate spline spaces, J. Approx. Theory. 111 (2001), 267-297.

Abstract: We present an algorithm for constructing stable local bases for the spaces ${\cal S}_d^r(\triangle)$ of multivariate polynomial splines of smoothness $r\ge1$ and degree $d\ge r2^n+1$ on an arbitrary triangulation $\triangle$ of a bounded polyhedral domain $\Omega\subset\RR^n$, $n\ge2$.

Preprint version available:    pdf