NDLI: Least-Squares Methods for Linear Elasticity

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Starke, Gerhard Cai, Zhiqiang
Copyright Year	2004
Abstract	This paper develops least-squares methods for the solution of linear elastic problems in both two and three dimensions. Our main approach is defined by simply applying the L2 norm least-squares principle to a stress-displacement system: the constitutive and the equilibrium equations. It is shown that the homogeneous least-squares functional is elliptic and continuous in the $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$ norm. This immediately implies optimal error estimates for finite element subspaces of $H({\rm div};\,\Omega)^d \times H^1(\Omega)^d$. It admits optimal multigrid solution methods as well if Raviart--Thomas finite element spaces are used to approximate the stress tensor. Our method does not degrade when the material properties approach the incompressible limit. Least-squares methods that impose boundary conditions weakly and use an inverse norm are also considered. Numerical results for a benchmark test problem of planar elasticity are included in order to illustrate the robustness of our method in the incompressible limit.
Starting Page	826
Ending Page	842
Page Count	17
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142902418357
e-ISSN	10957170
Issue Number	2
Volume Number	42
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	incompressible limit mixed finite element method linear elasticity Error bounds least-squares method Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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