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Simple finite element method in vorticity formulation for incompressible flows

Authors: Jian-Guo Liu and Weinan E
Journal: Math. Comp. 70 (2001), 579-593
MSC (2000): Primary 65M60, 76M10
Published electronically: March 3, 2000
MathSciNet review: 1710644
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Abstract: 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

Weinan E
Affiliation: Courant Institute of Mathematical Sciences, New York, NY 10012
MR Author ID: 214383
ORCID: 0000-0003-0272-9500

Keywords: Simple finite element method, Navier-Stokes equations, vorticity boundary conditions, error analysis
Received by editor(s): June 8, 1999
Published electronically: March 3, 2000
Additional Notes: JGL was supported in parts by NSF grant DMS-9805621.
Article copyright: © Copyright 2000 American Mathematical Society