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

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摘要

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.

论文关键词:Mixed FEM,Elasticity system,Lagrange multipliers,Mesh refinements,Hybrid method

论文评审过程:Received 2 October 2006, Revised 7 September 2007, Available online 17 November 2007.

论文官网地址:https://doi.org/10.1016/j.cam.2007.10.061