四边形非协调元方法逼近弹性和Stokes 问题
pproximation of elasticity and Stokes flow by quadrilateral nonconforming elements
本文研究了由 DUAN 和 LIANG 在 [Math. Comp., 73(2003), pp. 1-18] 提出的一个任意形正则四边形网格上的非协调元在线弹性问题和Stokes 问题的有限元方法数值求解的应用及其分析。建立了稳定性,获得了误差估计。该有限元方法适合于几乎不可压缩弹性问题和各种边界条件。也研究了离散 Korn 不等式及其新的证明。
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.
段火元
数学力学
计算数学 弹性问题 Stokes 问题 四边形网格非协调元$L^2$ 投影 Korn 不等式稳定性 误差估计Locking 现象一致收敛性
omputational Mathematics elasticity Stokes flow quadrilateral mesh nonconforming element $L^2$ projection Korn's inequality stability error estimates locking uniform convergence
段火元.四边形非协调元方法逼近弹性和Stokes 问题[EB/OL].(2015-11-12)[2025-08-16].http://www.paper.edu.cn/releasepaper/content/201511-174.点此复制
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