ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES

By Yuri Bazilevs, L. Beirão da Veiga, J. Cottrell, Thomas J. R. Hughes, Giancarlo Sangalli. 2006

797 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/49ffac5ee4b8df73824c52c0f25ed634035ef78b

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Citations in the corpus

A hierarchical approach to adaptive local refinement in isogeometric analysis (2011, background): “This extra smoothness leads in many cases to better convergence properties [21] and is also valuable when dealing with partial differential equations that demand for H 2 -regularity, such as plate and certain shell problems.”
Studies of Refinement and Continuity in Isogeometric Structural Analysis (Preprint) (2007, background): “It is clear from the studies described herein, and those in our o ther recent papers [ 1 , 3, 7], that the potential is very significant.”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “The theory of h-refinement of isogeometric spaces and methods, that is, the study of convergence that is achieved by refining the mesh, was developed in Bazilevs et al. (2006) and Beirão da Veiga, Cho and Sangalli (2012c), the latter covering anisotropic refinement.”
Isogeometric analysis of 2D gradient elasticity (2011, methodology): “A mathematical analysis of the isogeometric NURBSbased approach was performed in [ 14 ].”
Isogeometric analysis in electromagnetics: B-splines approximation (2010, methodology): “The approximation analysis of this scheme is carried out in Section 4 following the results of [4].”
Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, methodology): “The discretization error in Strang’s lemma is bounded by |u∗ − uh|1,Ω ≤ C3h , (31) where the constant C3 is independent of h, see [3].”
Adaptive isogeometric analysis by local h-refinement with T-splines (2010, background): “This also means that the convergence analysis of [3] applies in this case.”
Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow (2006, methodology): “Mathematical theory of isogeometric analysis for h-refined meshes may be found in the recent work of Bazilevs et al. [ 2 ].”
NURBS-based isogeometric analysis for the computation of flows about rotating components (2008, methodology): “(For background on NURBS the reader is referred to [13, 16,25,26], while the basics of NURBS-based isogeometric analysis are outlined in the original papers [4, 6 ,14,22].) We use the fact that NURBS, in contrast to standard finite elements, are capable of exactly representing all conic sections,inc”
Isogeometric design of elastic arches for maximum fundamental frequency (2011, background): “The superiority of the isogeometric framework over standard polynomial-based finite element analysis is argued from numerous perspectives as discussed in Bazilevs et al. (2006) and Evans et al. (2009).”