期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 39, 期 1, 页码 241-261出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2019010
关键词
Isogeometric analysis; adaptive methods; error estimate; hierarchical splines; THB-splines
资金
- ERC Advanced Grant CHANGE [694515]
- Istituto di Matematica Applicata e Tecnologie Informatiche del CNR, Pavia, Italy
- Istituto Nazionale di Alta Matematica (INdAM) through Finanziamenti Premiali MATHTECH
- MIUR Futuro in Ricerca project DREAMS [RBFR13FBI3]
- INdAM through Finanziamenti Premiali SUNRISE
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.
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