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Linear finite element methods for planar linear elasticity. (English) Zbl 0766.73060
Summary: A linear nonconforming (conforming) displacement finite element method for the pure displacement (pure traction) problem in two-dimensional linear elasticity for a homogeneous isotropic elastic material is considered. In the case of a convex polygonal configuration domain, \({\mathcal O}(h)\) (\({\mathcal O}(h^ 2)\)) error estimates in the energy \((L^ 2)\) norm are obtained. The convergence rate does not deteriorate for nearly incompressible material. Furthermore, the convergence analysis does not rely on the theory of saddle point problems.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74B05 Classical linear elasticity
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