The Convergence Rate and Necessary-and-Sufficient Condition for the Consistency of Isogeometric Collocation Method

TL;DR

This paper analyzes the convergence rate of the isogeometric collocation method and establishes the necessary and sufficient conditions for its consistency, enhancing the theoretical understanding of this practical numerical technique.

Contribution

It provides the first theoretical derivation of the convergence rate and the necessary and sufficient condition for the consistency of the IGA-C method.

Findings

Convergence rate formula for IGA-C established

Necessary and sufficient condition for IGA-C consistency derived

Advances the numerical analysis of isogeometric collocation methods

Abstract

Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency, only a little theoretical results have been established on the numerical analysis of the IGA-C method. In this paper, we deduce the convergence rate of the consistency of the IGA-C method. Moreover, based on the formula of the convergence rate, the necessary and sufficient condition for the consistency of the IGA-C method is developed. These results advance the numerical analysis of the IGA-C method.