An adaptive least squares mixed finite element method for the stress-displacement formulation of linear elasticity

A least-squares mixed finite element method for linear elasticity, based on a stress-displacement formulation, is investigated in terms of computational efficiency. For the stress approximation quadratic Raviart-Thomas elements are used and these are coupled with the quadratic nonconforming finite element spaces of Fortin and Soulie for approximating the displacement. The local evaluation of the least-squares functional serves as an a posteriori error estimator to be used in an adaptive refinement algorithm. We present computational results for a benchmark test problem of planar elasticity including nearly incompressible material parameters in order to verify the effectiveness of our adaptive strategy. For comparison, conforming quadratic finite elements are also used for the displacement approximation showing convergence orders similar to the nonconforming case, which are, however, not independent of the Lame parameters. (C) 2004 Wiley Periodicals. Inc.