| 平面线弹性纯位移边值问题低阶非协调矩形元的Robust多重网格方法 |
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| 引用本文： | 韩研,陈金如.平面线弹性纯位移边值问题低阶非协调矩形元的Robust多重网格方法[J].高等学校计算数学学报,2011,33(2):178-192. |
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| 作者姓名： | 韩研 陈金如 |
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| 作者单位： | 1. 江苏省大规模复杂系统数值模拟重点实验室
2. 南京师范大学数学科学学院,南京,210046 |
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| 摘 要： | 1引 言
对于各向同性,均匀介质的平面线弹性问题,当Lamé常数λ→∞(泊松率v→0.5)时,即对于几乎不可压介质,通常的协调有限元格式的解往往不再收敛到原问题的解,或者达不到最优收敛阶,这就是所谓的闭锁现象(见3],7],8]及10]).究其原因,在通常的有限元分析中,其误差估计的系数与λ有关,当λ→∞时,该系数将趋于无穷大.因此为克服闭锁现象就需要构造特殊的有限元格式,使得当λ→∞时,有限元逼近解仍然收敛到原问题的解.
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| 关 键 词： | 误差估计 边值问题 非协调元 多重网格算法 位移边界条件 多重网格方法 矩形元 线弹性 无闭锁 |
A ROBUST MULTIGRID METHOD FOR LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT FOR THE PURE DISPLACEMENT BOUNDARY VALUE PROBLEM IN PLANAR LINEAR ELASTICITY |
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| Han Yan,Chen Jinru.A ROBUST MULTIGRID METHOD FOR LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT FOR THE PURE DISPLACEMENT BOUNDARY VALUE PROBLEM IN PLANAR LINEAR ELASTICITY[J].Numerical Mathematics A Journal of Chinese Universities,2011,33(2):178-192. |
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| Authors: | Han Yan Chen Jinru |
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| Institution: | Han Yan Chen Jinru (Jiangsu Key Laboratory for NSLSCS,School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046) |
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| Abstract: | In this paper,a robust multigrid method is developed for a low order nonconforming rectangular finite element for the pure displacement boundary value problem in planar linear elasticity.Based on the mixed formulation,we approximate the displacement by the low order nonconforming rectangular finite elements proposed in20],and the pressure by piecewise constants.We show that the mixed method is stable.Also we propose a W-cycle multigrid for mixed method and prove that the convergence of the W-cycle multigri... |
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| Keywords: | planar linear elasticity pure displacement mixed finite element nonconforming rectangular finite element multigird |
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