Local approximation operators on box meshes

TL;DR

This paper investigates the approximation capabilities of tensor product polynomial spaces on box meshes, emphasizing error estimates in Lebesgue norms and demonstrating exponential convergence for analytic functions, relevant to IsoGeometric Analysis.

Contribution

It provides new error estimates for tensor product polynomial approximations on box meshes, including local, global, and Sobolev seminorms, with a focus on applications to IGA.

Findings

Exponential convergence for analytic functions

Error estimates in Lebesgue norms

Analysis of local and global approximation properties

Abstract

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