Approximation properties of isogeometric function spaces on singularly parameterized domains

TL;DR

This paper establishes approximation error bounds for isogeometric function spaces on singularly parameterized domains, specifically those derived from reparameterized triangular patches, ensuring optimal convergence.

Contribution

It provides the first rigorous proof of approximation error bounds for isogeometric discretizations on singularly parameterized domains derived from triangular patches.

Findings

Error bounds are established for isogeometric functions on singular domains.

Optimal convergence rates are guaranteed under certain regularity conditions.

The results extend the theoretical understanding of isogeometric analysis on complex geometries.

Abstract

We study approximation error bounds of isogeometric function spaces on a specific type of singularly parameterized domains. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider domains where one edge of the parameter domain is mapped onto one point in physical space. To be more precise, in our configuration the singular patch is derived from a reparameterization of a regular triangular patch. On such a domain one can define an isogeometric function space fulfilling certain regularity criteria that guarantee optimal convergence. The main contribution of this paper is to prove approximation error bounds for the previously defined class of isogeometric discretizations.