Polynomial preserving recovery for PHT-splines

TL;DR

This paper introduces a polynomial preserving recovery method for PHT-splines in isogeometric analysis, enhancing gradient approximation accuracy without relying on superconvergent point data, and supports adaptive refinement.

Contribution

It develops a superconvergent gradient recovery technique for PHT-splines that leverages local properties and error estimates, improving accuracy and enabling adaptive refinement.

Findings

Superconvergence of the recovered gradient on translation invariant meshes.

Effective a posteriori error estimator for adaptive refinement.

Numerical results confirm theoretical superconvergence and accuracy improvements.

Abstract

We propose a polynomial preserving recovery method for PHT-splines within isogeometric analysis to obtain more accurate gradient approximations. The method fully exploits the local interpolation properties of PHT-splines and avoids the need for information on gradient superconvergent points. By leveraging the superconvergence argument of difference quotients and the interior error estimate, we establish the superconvergence property of the recovered gradient on translation invariant meshes. As a byproduct, a recovery-based a posteriori error estimator is developed for adaptive refinement. Numerical results confirm the theoretical findings and demonstrate the effectiveness of the proposed method.