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Mathematics of Computation

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Simple finite element method in vorticity formulation for incompressible flows
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by Jian-Guo Liu and Weinan E PDF
Math. Comp. 70 (2001), 579-593 Request permission


A very simple and efficient finite element method is introduced for two and three dimensional viscous incompressible flows using the vorticity formulation. This method relies on recasting the traditional finite element method in the spirit of the high order accurate finite difference methods introduced by the authors in another work. Optimal accuracy of arbitrary order can be achieved using standard finite element or spectral elements. The method is convectively stable and is particularly suited for moderate to high Reynolds number flows.
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Additional Information
  • Jian-Guo Liu
  • Affiliation: Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742
  • MR Author ID: 233036
  • ORCID: 0000-0002-9911-4045
  • Email:
  • Weinan E
  • Affiliation: Courant Institute of Mathematical Sciences, New York, NY 10012
  • MR Author ID: 214383
  • ORCID: 0000-0003-0272-9500
  • Email:
  • Received by editor(s): June 8, 1999
  • Published electronically: March 3, 2000
  • Additional Notes: JGL was supported in parts by NSF grant DMS-9805621.
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 579-593
  • MSC (2000): Primary 65M60, 76M10
  • DOI:
  • MathSciNet review: 1710644