dc.description.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. | |