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This paper analyzes the approximation properties of spaces of piece-wisetensor product polynomials over box meshes with a focus on application toIsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms.Estimates of different types are considered: local and global, with full orreduced Sobolev seminorms. Attention is also paid to the dependence on thedegree and exponential convergence is proved for the approximation of analyticfunctions.

Local approximation operators on box meshes