Local approximation from spline spaces on box meshes

This paper analyzes the approximation properties of spaces of piecewise tensor product polynomials over box meshes with a focus on application to isogeometric analysis. Local and global error bounds with respect to Sobolev or reduced seminorms are provided. Attention is also paid to the dependence on the degree, and exponential convergence is proved for the approximation of analytic functions in the absence of non-convex extended supports.