000263433 001__ 263433
000263433 005__ 20190619220155.0
000263433 022__ $$a1078-0947
000263433 022__ $$a1553-5231
000263433 02470 $$a000448406700010$$2isi
000263433 0247_ $$a10.3934/dcds.2019010$$2doi
000263433 037__ $$aARTICLE
000263433 245__ $$aAdaptive Isogeometric Methods With Hierarchical Splines: An Overview
000263433 260__ $$c2019$$aSpringfield$$bAMER INST MATHEMATICAL SCIENCES-AIMS
000263433 269__ $$a2019-01-01
000263433 336__ $$aJournal Articles
000263433 520__ $$aWe consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates of the AIGM can be proved when suitable approximation classes are considered. This is in line with the theory of adaptive methods developed for finite elements, recently well re- viewed in [43]. The important output of our analysis is the definition of classes of admissibility for meshes underlying hierarchical splines and the design of an optimal adaptive strategy based on these classes of meshes. The adaptivity analysis is validated on a selection of numerical tests. We also compare the results obtained with suitably graded meshes related to different classes of admissibility for 2D and 3D configurations.
000263433 650__ $$aMathematics, Applied
000263433 650__ $$aMathematics
000263433 650__ $$aMathematics
000263433 6531_ $$aisogeometric analysis
000263433 6531_ $$aadaptive methods
000263433 6531_ $$aerror estimate
000263433 6531_ $$ahierarchical splines
000263433 6531_ $$athb-splines
000263433 6531_ $$asuitable t-splines
000263433 6531_ $$aboundary-element methods
000263433 6531_ $$alr b-splines
000263433 6531_ $$alinear independence
000263433 6531_ $$aoptimal convergence
000263433 6531_ $$alocal refinement
000263433 6531_ $$aspaces
000263433 6531_ $$adefinition
000263433 6531_ $$aalgorithms
000263433 6531_ $$adesign
000263433 700__ $$aBracco, Cesare
000263433 700__ $$g271675$$0250290$$aBuffa, Annalisa
000263433 700__ $$aGiannelli, Carlotta
000263433 700__ $$aVazquez, Rafael$$0250696$$g279669
000263433 773__ $$k1$$j39$$q241-261$$tDiscrete And Continuous Dynamical Systems
000263433 8560_ $$fpablo.antolin@epfl.ch
000263433 909C0 $$yApproved$$pMNS$$xU13308$$mpablo.antolin@epfl.ch$$zJunod, Julien$$0252586
000263433 909CO $$particle$$ooai:infoscience.epfl.ch:263433$$pSB
000263433 961__ $$afantin.reichler@epfl.ch
000263433 973__ $$aEPFL$$sPUBLISHED$$rREVIEWED
000263433 980__ $$aARTICLE
000263433 980__ $$aWoS
000263433 981__ $$aoverwrite