Mixed isogeometric finite cell methods for the stokes problem

T. Hoang, C.V. Verhoosel, F. Auricchio, E.H. van Brummelen, A. Reali

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Abstract

We study the application of the Isogeometric Finite Cell Method (IGA-FCM) to mixed formulations in the context of the Stokes problem. We investigate the performance of the IGA-FCM when utilizing some isogeometric mixed finite elements, namely: Taylor-Hood, Sub-grid, Raviart-Thomas, and Nédélec elements. These element families have been demonstrated to perform well in the case of conforming meshes, but their applicability in the cut-cell context is still unclear. Dirichlet boundary conditions are imposed by Nitsche's method. Numerical test problems are performed, with a detailed study of the discrete inf-sup stability constants and of the convergence behavior under uniform mesh refinement.

Original languageEnglish
Pages (from-to)400–423
Number of pages24
JournalComputer Methods in Applied Mechanics and Engineering
Volume316
DOIs
Publication statusPublished - 2017

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Keywords

  • Fictitious domain
  • Finite cell method
  • Immersed boundary method
  • Isogeometric analysis
  • Mixed formulations
  • Stokes

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