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.

中文翻译：

---

框网格上样条空间的局部逼近

本文分析了盒式网格上分段张量积多项式空间的逼近性质，重点是在等几何分析中的应用。提供了有关Sobolev或简化的半范数的局部和全局误差范围。还应注意对度的依赖性，并且在没有非凸扩展支撑的情况下，证明了解析函数逼近的指数收敛性。