Mixed finite elements for elasticity on quadrilateral meshes
Mixed finite elements for elasticity on quadrilateral meshes
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DOI：
10.1007/s10444-014-9376-x
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发表时间：
2013-06
影响因子：
1.7
通讯作者：
D. Arnold;Gerard Awanou;W. Qiu
中科院分区：
文献类型：
--
作者：
D. Arnold;Gerard Awanou;W. Qiu
本文提出了平面线弹性问题在一般四边形网格上的稳定混合元。应力张量的对称性是弱的，因此有三个主要变量，应力张量，位移矢量场和标量旋转。我们发展和分析了一个稳定的方法族，指标为整数r ≥ 2，所有变量的收敛速度为r阶的L2范数。该方法使用Raviart-Thomas元素的应力，分段张量积多项式的位移，和分段多项式的旋转。我们还提出了一个简单的一阶元素，不属于这个家庭。它使用最低阶BDM单元的应力，和分段常数的位移和旋转，并实现一阶收敛的所有三个变量。
We present stable mixed finite elements for planar linear elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the scalar rotation. We develop and analyze a stable family of methods, indexed by an integerr≥ 2 and with rate of convergence in theL2norm of orderrfor all the variables. The methods use Raviart–Thomas elements for the stress, piecewise tensor product polynomials for the displacement, and piecewise polynomials for the rotation. We also present a simple first order element, not belonging to this family. It uses the lowest order BDM elements for the stress, and piecewise constants for the displacement and rotation, and achieves first order convergence for all three variables.