A collocated isogeometric finite element method based on Gauss–Lobatto Lagrange extraction of splines

Generalizing the concept of Bézier extraction, we introduce an extraction operator that links C⁰ Gauss–Lobatto Lagrange functions with smooth splines. This opens the door for collocated isogeometric analysis that combines the accuracy of the Galerkin method with collocation-type formation and assembly procedures. We present the key ingredients of the technology, i.e. integration by parts and the weighted residual form, the interaction of Gauss–Lobatto Lagrange extraction with Gauss–Lobatto quadrature, and symmetrization with the ultra-weak formulation. We compare the new method with standard isogeometric Galerkin and isogeometric point-collocation methods for spline discretizations in three dimensions.