IsoGeometric Analysis: Stable elements for the 2D Stokes equation

By Annalisa Buffa, Carlo de Falco, Giancarlo Sangalli. 2011

213 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/157d5837d53a04bc1f64bc85f5b05db26b120ca8

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “We however remark that, using diﬀerent discretization methodologies, some divergence-free methods have already proposed in the literature (for instance, see [23,25,28,29,35,36]).”
Isogeometric finite element analysis of poroelasticity (2013, background): “Although the approach could be further improved in the sense that in the current formulation the orders of interpolation of the displacements and the pressure have been taken equal [20, 21], the advantages over conventional FEA become clear from simple examples.”
Discretizations in isogeometric analysis of Navier-Stokes flow (2011, unknown): “Keywords: isogeometric analysis, fluid mechanics, Navier-Stokes flow, inf-sup stability, lid-driven square cavity”
Isogeometric discretizations of the Stokes problem: stability analysis by the macroelement technique (2013, methodology): “…is having a growing impact on several fields, from fluid dynamics (Bazilevs et al., 2007, 2008, 2010; Zhang et al., 2007; Gomez et al., 2010; Buffa et al., 2011) to structural mechanics (Cottrell et al., 2006; Auricchio et al., 2007; Lipton et al., 2010) and electromagnetics (Buffa et al.,…”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “The proof can be found in Buffa et al. (2011b) and follows the same arguments used for the convergence of finite elements in Hiptmair (2002, Section 5).”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, methodology): “In the context of Isogeometric Analysis, a few choices of spline based discrete pairs of spaces (Vh, Qh) which satisfy (4) have been presented in Buffa et al. [12].”
ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS (2013, methodology): “1 Two-dimensional Manufactured Solution As a first numerical experiment, we consider a two-dimensional manufactured vortex solution that was originally presented in [8].”