Optimal-order isogeometric analysis and isogeometric collocation at Galerkin superconvergent points

Abstract

Isogeometric analysis with full quadrature yields optimal convergence rates but require higher computational cost than necessary for splines of maximal continuity. In this thesis two such methods, the weak variational method and the weighted residual method, are presented. These methods are compared with three isogeometric collocation method, one collocated at Greville points and the others at different sets of superconvergent points. Isogeometric collocation at superconvergent point may yield one order suboptimal continuity in L 2 -norm for even polynomial orders but otherwise provide the same accuracy as the isogeometric analysis methods, with just one evaluation point per degree of freedom. Correct selection of superconvergent points are vital to obtain these rates.