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.