NDLI: First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Parter, Seymour V. Manteuffel, Thomas A. McCormick, Stephen F. Cai, Zhiqiang
Copyright Year	1998
Abstract	This paper develops two first-order system least-squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement (which immediately yield deformation and stress), then for the displacement itself (if desired). One approach, which uses L2 norms to define the FOSLS functional, is shown under certain H2 regularity assumptions to admit optimal H1 -like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H-1 norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L2 norm and for displacement in an H1 norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.
Starting Page	320
Ending Page	335
Page Count	16
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142995294930
e-ISSN	10957170
Issue Number	1
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	least-squares discretization Other matrix algorithms Poisson ratio Iterative methods for linear systems multigrid linear elasticity pure traction
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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