Bracco, Cesare
Buffa, Annalisa
Giannelli, Carlotta
Vazquez, Rafael
Adaptive Isogeometric Methods With Hierarchical Splines: An Overview
Discrete And Continuous Dynamical Systems
1078-0947
10.3934/dcds.2019010
39
1
241-261
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.
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;
AMER INST MATHEMATICAL SCIENCES-AIMS
Springfield
2019