A mixed least squares method for solving problems in linear elasticity: theoretical study

In a previous paper we proposed a mixed least squares method for solving problems in linear elasticity. The solution to the equations of linear elasticity was obtained via minimization of a least squares functional depending on displacements and stresses. The performance of the method was tested num...

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Bibliographic Details
Published in:Computational mechanics 2002-10, Vol.29 (4-5), p.332-339
Main Authors: TCHONKOVA, M, STURE, S
Format: Article
Language:English
Subjects:
Compressibility
Computational fluid dynamics
Computational techniques
Elasticity
Exact sciences and technology
Exact solutions
Finite element method
Finite-element and galerkin methods
Fundamental areas of phenomenology (including applications)
Least squares method
Mathematical methods in physics
Mixed methods research
Physics
Polynomials
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Uniqueness
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Summary:In a previous paper we proposed a mixed least squares method for solving problems in linear elasticity. The solution to the equations of linear elasticity was obtained via minimization of a least squares functional depending on displacements and stresses. The performance of the method was tested numerically for low order elements for classical examples with well known analytical solutions. In this paper we derive a condition for the existence and uniqueness of the solution of the discrete problem for both compressible and incompressible cases, and verify the uniqueness of the solution analytically for two low order piece-wise polynomial FEM spaces.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-002-0346-7