An adaptive isogeometric analysis collocation method with a recovery-based error estimator

Abstract

In this paper, we propose an enhanced isogeometric analysis (IGA) collocation method. It is well known that the location of the collocation points plays an important role in the accuracy and stability of IGA collocation methods. This is particularly true for non-uniform meshes and domains generated from multi-patch geometries. We present an enhanced collocation method based on Gauss points, which has improved accuracy as compared to using C1 splines and a recovery-based error estimator that can be derived by sampling the solution at particular points in the domain. Adaptivity is implemented using a hierarchical spline basis, which satisfies the C1 continuity requirement. The proposed approach has been tested by several benchmark problems, including multipatch domains and geometries with re-entrant corners.