共查询到19条相似文献,搜索用时 78 毫秒
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关于板—梁组合构件的有限元方法,文[1]对对称梁的情形已进行了讨论.我们处理这类问题的基本想法,是通过各组合件的应变能的迭加以形成组合构件的总应变能,由此得到的有限元解法,可使编制程序时具有一定的通用性;由[1]还可以看出,基于这种自然的想法,对于组合构件来说,有限元往往是非协调的,因此研究组合构件非协 相似文献
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本文研究对称椭圆特征值问题的有限元后验误差估计,包括协调元和非协调元,具有下列特色:(1)对协调/非协调元建立了有限元特征函数uh的误差与相应的边值问题有限元解的误差在局部能量模意义下的恒等关系式,该边值问题的右端为有限元特征值λh与uh的乘积,有限元解恰好为uh.从而边值问题有限元解在能量模意义下的局部后验误差指示子,包括残差型和重构型后验误差指示子,成为有限元特征函数在能量模意义下的局部后验误差指示子.(2)讨论了协调有限元特征函数的基于插值后处理的梯度重构型后验误差估计,对有限元特征函数的导数得到了最大模意义下的渐近准确局部后验误差指示子. 相似文献
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《应用数学与计算数学学报》2016,(4)
利用非协调自适应有限元方法求解一类非线性退化凸极值问题.该方法遵循求解、估计、标注、加密四个步骤,给出了后验误差估计.数值算例验证了理论分析结果. 相似文献
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非协调元特征值渐近下界 总被引:1,自引:1,他引:0
利用有限元收敛速度下界的结果获得某些非协调元方法新的Aubin-Nitsche估计形式,然后再结合非协调元特征值的展开式获得不需要额外条件下非协调元特征值渐近下界的结果. 相似文献
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《数学的实践与认识》2015,(9)
用有限元方法计算椭圆型界面特征值问题,实验数据显示近似特征值的变化规律:界面特征值问题中系数的间断性对协调和非协调Crouzeix-Raviart有限元特征值的收敛性并无影响,而且对协调有限元特征值外推以后得到高精度的解,相应的外推值还提供特征值下界;Crouzeix-Raviart元特征值提供特征值下界,这对一般有界区域如"镂空"型区域也成立.另外,还展示近似特征函数的图形. 相似文献
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研究了非协调有限元逼近非单调型拟线性椭圆问题,使用超收敛误差估计技巧,得出该问题光滑解和有限元解之间存在的超收敛关系. 相似文献
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应用三维EQ1rot元、三维Crouzeix-Raviart元、八节点等参数元、四面体线性元计算三维Poisson方程的近似特征值.计算结果表明:三维EQ1rot元和三维Crouzeix-Raviart元特征值下逼近准确特征值,八节点等参数元、四面体线性元特征值上逼近准确特征值,三维EQr1ot元和三维Crouzeix-Raviart元外推特征值下逼近准确特征值.计算结果还表明三维Crouzeix-Raviart元是一种计算效率较高的非协调元. 相似文献
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非正则条件下类Wilson元的构造及其应用 总被引:3,自引:1,他引:2
本文在非正则性条件下,研究了窄四边形上的类Wilson元。通过参考元上类Wilson元的构造,证明了由此产生的有限元对任意窄四边形剖分通过Irons分片检查,得到了二阶问题的误差估计。结果表明,该单元的收敛性质与Wilson元的类似。 相似文献
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Shangyou Zhang Zhimin Zhang Qingsong Zou 《Numerical Methods for Partial Differential Equations》2017,33(6):1859-1883
We propose a local postprocessing method to get a new finite element solution whose flux is conservative element‐wise. First, we use the so‐called polynomial preserving recovery (postprocessing) technique to obtain a higher order flux which is continuous across the element boundary. Then, we use special bubble functions, which have a nonzero flux only on one face‐edge or face‐triangle of each element, to correct the finite element solution element by element, guided by the above super‐convergent flux and the element mass. The new finite element solution preserves mass element‐wise and retains the quasioptimality in approximation. The method produces a conservative flux, of high‐order accuracy, satisfying the constitutive law. Numerical tests in 2D and 3D are presented.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1859–1883, 2017 相似文献
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Rail-bridge coupling element of unequal lengths for analysing train-track-bridge interaction systems
This paper presents a rail-bridge coupling element of unequal lengths, in which the length of a bridge element is longer than that of a rail element, to investigate the dynamic problem of train-track-bridge interaction systems. The equation of motion in matrix form is given for a train-track-bridge interaction system with the proposed element. The first two numerical examples with two types of bridge models are chosen to illustrate the application of the proposed element. The results show that, for the same length of rail element, (1) the dynamic responses of train, track and bridge obtained by the proposed element are almost identical to those obtained by the rail-bridge coupling element of equal length, and (2) compared with the rail-bridge coupling element of equal length, the proposed element can help to save computer time. Furthermore, the influence of the length of rail element on the dynamic responses of rail is significant. However, the influence of the length of rail element on the dynamic responses of bridge is insignificant. Therefore, the proposed element with a shorter rail element and a longer bridge element may be adopted to study the dynamic responses of a train-track-bridge interaction system. The last numerical example is to investigate the effects of two types of track models on the dynamic responses of vehicle, rail and bridge. The results show that: (1) there are differences of the dynamic responses of vehicle, rail and bridge based on the single-layer and double-layer track models, (2) the maximum differences increase with the increase of the mass of sleeper, (3) the double-layer track model is more accurate. 相似文献
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1. IntroductionIn the numerical simulation of the Navier-Stokes equations one encounters three seriousdifficulties in the case of large Reynolds numbers f the treatment of the incomPressibility con-dition divu = 0, the treatment of the noIilinear terms and the large time integration. For thetreatment of the incoInPressibility condition, one use the penalty method in the case of finiteelemellts [1--2l and for the treatmen of the noulinar terms and the large tfor integration, oneuse the nonlin… 相似文献