A new dual-mixed finite element method for the plane linear elasticity problem with pure traction boundary conditions. (English) Zbl 1169.74601

Summary: 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 \(L^{2}\)-norm. Finally, several numerical results illustrating the good performance of the mixed finite element scheme are reported.


74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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