Dual mixed finite element methods for the elasticity problem with Lagrange multipliers

We study a dual mixed formulation of the elasticity system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The (essential) Neumann boundary conditions (or traction boundary condition) are imposed using a discontinuous Lagrange multiplier correspondi...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2008-11, Vol.221 (1), p.234-260
Main Authors: Boulaajine, L., Nicaise, S., Paquet, L., Rafilipojaona
Format: Article
Language:English
Subjects:
Acceleration of convergence
Elasticity system
Exact sciences and technology
Hybrid method
Lagrange multipliers
Mathematical analysis
Mathematics
Mesh refinements
Mixed FEM
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
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Summary:We study a dual mixed formulation of the elasticity system in a polygonal domain of the plane with mixed boundary conditions and its numerical approximation. The (essential) Neumann boundary conditions (or traction boundary condition) are imposed using a discontinuous Lagrange multiplier corresponding to the trace of the displacement field. Moreover, a strain tensor is introduced as a new unknown and its symmetry is relaxed, also by the use of a Lagrange multiplier (the rotation). The singular behaviour of the solution requires us to use refined meshes to restore optimal rates of convergence. Uniform error estimates in the Lamé coefficient λ are obtained for large λ . The hybridization of the problem is performed and numerical tests are presented confirming our theoretical results.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.10.061