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

  • Authors:

  • L. Boulaajine;S. Nicaise;L. Paquet; Rafilipojaona

  • Affiliations:

  • INRIA - Projet Gamma, Domaine de Voluceau, Rocquencourt - B.P. 105, 78153 Le Chesnay Cedex, France;Université de Valenciennes et du Hainaut Cambrésis, LAMAV, ISTV, F-59313 - Valenciennes Cedex 9, France;Université de Valenciennes et du Hainaut Cambrésis, LAMAV, ISTV, F-59313 - Valenciennes Cedex 9, France;Université de Fianarantsoa, Faculté des Sciences, B.P. 1486, Fianarantsoa 301, Madagascar

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2008

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Abstract

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 Lame coefficient @l are obtained for large @l. The hybridization of the problem is performed and numerical tests are presented confirming our theoretical results.