Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 79, Issue 8, Pages 2276-2303Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2019.10.028
Keywords
Hierarchical spaces; Splines bases; Optimality for adaptive methods
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Funding
- Agencia Nacional de Promocion Cientifica y Tecnologica [PICT-2014-2522, PICT-20161983]
- CONICET [PIP 2015 11220150100661]
- Universidad Nacional del Litoral [CAI+D 2016-50420150100022LI, 2016-50020150100074LI]
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We introduce a framework for spline spaces of hierarchical type, based on a parentchildren relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. This framework exploits the innate refinement by functions in the B-splines context, rather than by elements or cells, which is more natural in the finite element context. Furthermore, it entails a new language to handle hierarchical spline spaces, which allows to tackle fundamental questions in a very simple manner. For example, it makes it simple to create hierarchical bases with several desired properties with a refinement procedure which has linear complexity, i.e., the resulting bases have cardinality bounded by the number of initially marked functions. (C) 2019 Elsevier Ltd. All rights reserved.
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