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

Hansen, Silje Irene
Master thesis
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URI
http://hdl.handle.net/11250/2453099
Date
2016
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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.
Publisher
NTNU

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