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Anisotropic adaptivity for the finite element solutions of three‐dimensional convection‐dominated problems
Author(s) -
Walkley Mark,
Jimack Peter K.,
Berzins Martin
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.302
Subject(s) - finite element method , adaptive mesh refinement , isotropy , mesh generation , grid , convection , mathematics , boundary (topology) , computer science , anisotropy , geometry , mathematical optimization , minification , algorithm , mathematical analysis , mechanics , computational science , physics , optics , thermodynamics
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. Copyright © 2002 John Wiley & Sons, Ltd.