Bracco, Cesare
Buffa, Annalisa
Giannelli, Carlotta
Vazquez, Rafael
Adaptive Isogeometric Methods With Hierarchical Splines: An Overview
Discrete And Continuous Dynamical Systems
Discrete And Continuous Dynamical Systems
Discrete And Continuous Dynamical Systems
Discrete And Continuous Dynamical Systems
39
1
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
Mathematics, Applied
Mathematics
Mathematics
2019
2019
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.
AMER INST MATHEMATICAL SCIENCES-AIMS
1078-0947
Discrete And Continuous Dynamical Systems
Journal Articles
000448406700010