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| A finite element method is proposed and analyzed for elasticity problem and Stokes flow using the quadrilateral nonconforming element by DUAN and LIANG [Math. Comp., 73(2003), pp. 1-18]. The proposed finite element method is suitable for arbitrary shape-regular quadrilateral meshes. Various boundary conditions are allowed in the proposed method. Stability is established, and optimal error bounds are obtained. In particular, the proposed method renders a uniform convergence with respect to the Lam'{e} coefficient or Poisson ratio. In addition, new proofs are studied for discrete Korn's inequalities. |
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| Keywords:Computational Mathematics, elasticity, Stokes flow, quadrilateral mesh, nonconforming element, $L^2$ projection, Korn's inequality, stability, error estimates, locking, uniform convergence |
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