263433
20190619220155.0
1078-0947
1553-5231
isi
000448406700010
doi
10.3934/dcds.2019010
ARTICLE
Adaptive Isogeometric Methods With Hierarchical Splines: An Overview
Springfield
AMER INST MATHEMATICAL SCIENCES-AIMS
2019
2019-01-01
Journal Articles
We 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.
Mathematics, Applied
Mathematics
Mathematics
isogeometric analysis
adaptive methods
error estimate
hierarchical splines
thb-splines
suitable t-splines
boundary-element methods
lr b-splines
linear independence
optimal convergence
local refinement
spaces
definition
algorithms
design
Bracco, Cesare
250290
Buffa, Annalisa
271675
Giannelli, Carlotta
250696
Vazquez, Rafael
279669
39
1
241-261
Discrete And Continuous Dynamical Systems
pablo.antolin@epfl.ch
252586
pablo.antolin@epfl.ch
MNS
U13308
Approved
Junod, Julien
oai:infoscience.epfl.ch:263433
article
SB
fantin.reichler@epfl.ch
EPFL
REVIEWED
PUBLISHED
ARTICLE
WoS
overwrite