ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS

By John A. Evans, Thomas J. R. Hughes. 2013

169 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/e62e5d145c351ff07215ed3b15afcfb8fb149049

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Isogeometric Analysis and error estimates for high order partial differential equations in Fluid Dynamics (2014, methodology): “The analogies highlighted in Table 3 between our results and [22] could be explained by the fact that both the approaches consider NURBS–based IGA in the framework of the Galerkin method for the spatial approximation with the exact mass conservation property satisfied by construction.”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “We remark that the same space has been applied to the solution of incompressible Stokes and Navier–Stokes equations in Buffa et al. (2011a) and Evans and Hughes (2013a, 2013b, 2013c), to obtain numerical solutions which are pointwise divergence-free.”
On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime (2014, methodology): “This price, which by the way can be avoided completely by divergence-free mixed methods like the classical Scott-Vogelius element[49, 48, 41, 51] or more recent divergence-free discretization approaches[11, 12, 50, 20, 21, 22], is well-known in the finite element community as poor mass conservation ”
Divergence-conforming discretization for Stokes problem on locally refined meshes using LR B-splines (2015, methodology): “Later using the idea of div-compatible spline spaces presented in the setting of discrete differential forms [11], a series of isogeometric divergence conforming spline discretizations were derived to solve Stokes and Brinkman equations, steady and unsteady Navier-Stokes equations by Evans in [17, 1”
On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows (2015, background): “with Φ := {v ∈ L(2)(Ω) : curlv ∈ H(1)(Ω)} was recently proposed in [23] to derive stable pairs in an isogeometric framework.”