http://www.cnr.it/ontology/cnr/individuo/prodotto/ID31190
Isogeometric analysis: approximation, stability and error estimates for h-refined meshes (Articolo in rivista)
- Type
- Label
- Isogeometric analysis: approximation, stability and error estimates for h-refined meshes (Articolo in rivista) (literal)
- Anno
- 2006-01-01T00:00:00+01:00 (literal)
- Alternative label
Bazilevs Y., Beirao da Veiga L., Cottrell J.A., Hughes T.J.R., Sangalli G. (2006)
Isogeometric analysis: approximation, stability and error estimates for h-refined meshes
in Mathematical models and methods in applied sciences
(literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
- Bazilevs Y., Beirao da Veiga L., Cottrell J.A., Hughes T.J.R., Sangalli G. (literal)
- Pagina inizio
- Pagina fine
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- Rivista
- Note
- ISI Web of Science (WOS) (literal)
- Scopus (literal)
- Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
- Bazilevs e' ora alla University di San Diego (US)
Beirao da Veiga e' all' Universita' di Milano
Cottrell non e' piu' in Universita' (era al ICES nel 2006)
Hughes e' al ICES, University of TEXAS at Austin
Giancarlo Sangalli e' all'Universita' di Pavia (literal)
- Titolo
- Isogeometric analysis: approximation, stability and error estimates for h-refined meshes (literal)
- Abstract
- We begin the mathematical study of Isogeometric Analysis based on NURBS (nonuniform
rational B-splines). Isogeometric Analysis is a generalization of classical Finite
Element Analysis (FEA) which possesses improved properties. For example, NURBS
are capable of more precise geometric representation of complex objects and, in particular,
can exactly represent many commonly engineered shapes, such as cylinders,
spheres and tori. Isogeometric Analysis also simplifies mesh refinement because the
geometry is fixed at the coarsest level of refinement and is unchanged throughout
the refinement process. This eliminates geometrical errors and the necessity of linking
the refinement procedure to a CAD representation of the geometry, as in classical
FEA. In this work we study approximation and stability properties in the context of
h-refinement. We develop approximation estimates based on a new Bramble-Hilbert
lemma in so-called \"bent\" Sobolev spaces appropriate for NURBS approximations
and establish inverse estimates similar to those for finite elements. We apply the
theoretical results to several cases of interest including elasticity, isotropic incompressible
elasticity and Stokes flow, and advection-diffusion, and perform numerical
tests which corroborate the mathematical results. We also perform numerical calculations
that involve hypotheses outside our theory and these suggest that there are
many other interesting mathematical properties of Isogeometric Analysis yet to be
proved. (literal)
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