A quadrilateral nonconforming finite element for linear elasticity problem

In this paper, a four-parameter quadrilateral nonconforming finite element with DSP (double set parameters) is presented. Then we discuss the quadrilateral nonconforming finite element approximation to the linear elastic equations with pure displacement boundary. The optimal convergence rate of the method is established in the broken $H^1$ energy and $L^2$-norms, and in particular, the convergence is uniform with respect to the Lamé parameter $\lambda$. Also the performance of the scheme does not deteriorate as the material becomes nearly incompressible. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.

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