Adaptive isogeometric methods with hierarchical splines: error estimator and convergence (Q2788504)
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scientific article; zbMATH DE number 6542994
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Adaptive isogeometric methods with hierarchical splines: error estimator and convergence |
scientific article; zbMATH DE number 6542994 |
Statements
19 February 2016
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isogeometric analysis
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hierarchical splines
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adaptivity
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convergence
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error estimate
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Galerkin approximation
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Adaptive isogeometric methods with hierarchical splines: error estimator and convergence (English)
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The aim of the present paper is to define and study an adaptive isogeometric method (AIGM) based on hierarchical splines (cf. [\textit{C. Giannelli} et al., Adv. Comput. Math. 40, No. 2, 459--490 (2014; Zbl 1298.41010)] and [\textit{G. Kiss} et al., Graphical Models 76, 273--288 (2014)]). Based on the truncated basis for hierarchical splines with respect to some class of admissible meshes and a certain multilevel refinement, a posteriori residual-type estimators for the error associated to the Galerkin approximation of a simple model problem are given. The authors provide numerical analysis of the AIGM and convergence result together with the contraction of the quasi-error.
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