Abstract

In this paper we consider the stress-displacement-rotation formulation of the plane linear elasticity problem with pure traction boundary conditions and develop a new dual-mixed finite element method for approximating its solution. The main novelty of our approach lies on the weak enforcement of the non-homogeneous Neumann boundary condition through the introduction of the boundary trace of the displacement as a Lagrange multiplier. A suitable combination of PEERS and continuous piecewise linear functions on the boundary are employed to define the dual-mixed finite element scheme. We apply the classical Babuška-Brezzi theory to show the well-posedness of the continuous and discrete formulations. Then, we derive a priori rates of convergence of the method, including an estimate for the global error when the stresses are measured with the L2-norm. Finally, several numerical results illustrating the good performance of the mixed finite element scheme are reported. © 2007 Elsevier B.V. All rights reserved.