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A locking-free scheme of nonconforming rectangular finite element for the planar elasticity. (English) Zbl 1088.74046
Summary: We present a locking-free scheme of the lowest order for nonconforming rectangle finite element method for planar elasticity with the pure displacement boundary condition. Optimal order error estimate, uniform in the Lamé constant $$\lambda\in(0,\infty)$$, is obtained.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74B05 Classical linear elasticity 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs
##### Keywords:
optimal error estimate