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Anisotropic adaptivity for the finite element solutions of three-dimensional convection-dominated problems

Walkley, M., Jimack, P.K. and Berzins, M. (2002) Anisotropic adaptivity for the finite element solutions of three-dimensional convection-dominated problems. International Journal for Numerical Methods in Fluids, 40 (3-4). pp. 551-559. ISSN 0271-2091

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Abstract

Convection-dominated problems are typified by the presence of strongly directional features such as shock waves or boundary layers. Resolution of numerical solutions using an isotropic mesh can lead to unnecessary refinement in directions parallel to such features. This is particularly important in three dimensions where the grid size increases rapidly during conventional isotropic refinement procedures.

In this work, we investigate the use of adaptive finite element methods using anisotropic mesh refinement strategies for convection-dominated problems. The strategies considered here aim to resolve directional features without excessive resolution in other directions, and hence achieve accurate solutions more efficiently. Two such strategies are described here: the first based on minimization of the least-squares residual; the second based on minimizing a finite element error estimate. These are incorporated into an hr-adaptive finite element method and tested on a simple model problem.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 John Wiley & Sons, Ltd. This is an author produced version of a paper published in 'International Journal for Numerical Methods in Fluids'
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 21 Nov 2006
Last Modified: 05 Jun 2014 21:35
Published Version: http://dx.doi.org/10.1002/fld.302
Status: Published
Publisher: John Wiley & Sons, Ltd.
Refereed: Yes
Identification Number: 10.1002/fld.302
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1733

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