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Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method. 相似文献
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A Locking-Free Scheme of Nonconforming Rectangular Finite Element for the Planar Elasticity 总被引:1,自引:0,他引:1
Leiheng Wang & He Qi 《计算数学(英文版)》2004,22(5):641-650
In this paper, the authors present a locking-free scheme of the lowest order nonconforming rectangle finite element method for the planar elasticity with the pure displacement boundary condition. Optimal order error estimate, uniformly for the Laméconstant $\lambda\in(0,\infty)$ is obtained. 相似文献
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针对纯应力平面弹性问题构造了一个非协调矩形元.该单元满足离散的第二Korn不等式,并且关于λ有一致最优收敛阶,其误差的能量模和L2-模分别为O(h2)和O(h3) . 相似文献
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Two locking-free nonconforming finite elements are presented for three-dimensional elasticity problem with pure displacement boundary condition. Convergence rate of the elements are uniformly optimal with respect to λ. The energy norm and L2 norm errors are O(h2) and O(h3), respectively. Lastly, a numerical experiment is carried out, which coincides with the theoretical analysis. 相似文献
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In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition. 相似文献
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Shaochun Chen 《Journal of Computational and Applied Mathematics》2010,233(10):2534-2548
In this paper, we present two nonconforming finite elements for the pure displacement planar elasticity problem. Both of them are locking-free and have two order of convergence. Some numerical results attest the validity of our theoretical analysis. 相似文献
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A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM 总被引:2,自引:1,他引:1
The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value prob-lem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L2-norms are independent of the Lame parameterλ. 相似文献
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针对平面弹性问题构造了一个Locking-free的矩形非协调有限元,并证明该有限元格式关于λ有一致最优收敛阶,其离散误差的能量模为O(h2),L2模为O(h3).最后给出了数值实验对理论结果进行了验证. 相似文献
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In this paper,we extend two rectangular elements for Reissner-Mindlin plate[9] to the quadrilateral case,Optimal H^1 and L^2 error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition. 相似文献