Abstract: The Gaussian isogeometric analysis (IGA) collocation method was extended to arbitrary higher order polynomial degrees. The current IGA collocation method applied a new hierarchical basis over T-meshes (PHT-splines), which took advantage of the tensor product structure to prevent the decay phenomenon from happening in the original PHT basis. The improved method collocated at Gaussian points as the superconvergent points for the new PHT elements. Based on the new PHT basis, the current collocation method can be extended to arbitrary higher order approximation. In order to simplify the collocation boundary condition, a hybrid method was adopted to impose the boundary condition, using the Galerkin method for the boundary part and combing with the collocation solving system. The local refinement strategy was driven by a recovery-based error estimator that invoked computing an improved approximation without knowledge of the exact solution. The proposed collocation method can obtain the optimal convergent rates, compared with the IGA Galerkin method. 

Key words: isogeometric analysis, collocation method, PHT-splines, Gaussian collocation points, higher order elements, adaptive refinement