Optimal-order isogeometric analysis and isogeometric collocation at Galerkin superconvergent points
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Isogeometric analysis with full quadrature yields optimal convergence ratesbut require higher computational cost than necessary for splines of maximalcontinuity. In this thesis two such methods, the weak variational method andthe weighted residual method, are presented. These methods are compared withthree isogeometric collocation method, one collocated at Greville points and theothers at different sets of superconvergent points. Isogeometric collocation atsuperconvergent point may yield one order suboptimal continuity in L2-normfor even polynomial orders but otherwise provide the same accuracy as theisogeometric analysis methods, with just one evaluation point per degree offreedom. Correct selection of superconvergent points are vital to obtain theserates.