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1.
二阶问题的一个类Wilson非协调元   总被引:9,自引:0,他引:9  
§1.引言 Wilson元是工程计算中常用的一种非协调元,数值计算效果很好,但是Wilson元对于任意四边形网格却不能收敛.石钟慈在[1]中限制四边形单元剖分,要求四边形单元满足对角线中点距离d_K=o(h_K~2),而[2]—[3]则修改了双线性形式,即在刚度矩阵元素的计算中采用某种数值积分,这两种方法均使得Wilson元达到收敛.另外,通过改变形状函数,[4]—[5]提出了一个六参数非协调四边形单元QP6,它是推广的Wilson元.此元对任意四边形网格能够收敛,但其单元上的形状函数非常依赖单元本身.  相似文献   

2.
一类改进的Wilson任意四边形单元   总被引:24,自引:0,他引:24  
Wilson元是工程计算中数值效果很好的一种非协调元,但对任意四边形网格却不能收敛。石钟慈要求四边形单元满足对角线中点距离d_k=O(h_k~2),[2]、[3]提出了一个六参数非协调四边形单元。它对任意四边形网格收敛,但其单元上的形状函数非常依赖单元本  相似文献   

3.
一类六参数非协调任意凸四边形单元   总被引:5,自引:0,他引:5  
本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。  相似文献   

4.
通过对Q4元增加一个非协调高阶项.构造了一类新的非协调四边形单元,并证明由此产生的单元对任意四边形网格通过Irons分片检查和广义分片检查,且形状函敷不依赖于单元本身.QM5是其中的一个特例.数值结果表明,该类单元有很好的收敛效果.  相似文献   

5.
蔚喜军 《计算数学》1993,15(3):346-351
§1.引言 非协调Wilson有限元[1—3]对解弹性力学方程有实用价值,在工程上有用。本文分析Wilson元的多重网格法,给出用多重网格方法求得的近似解按L~2模和能量模的最佳收敛阶误差估计。对于W-循环,可以证明其计算量与离散空间的维数为同一量级O(N_k)。 考虑二阶椭圆Dirchlet边值问题:  相似文献   

6.
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  
李清善 《应用数学》2002,15(1):72-76
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   

7.
构造了一个用于对流扩散问题的任意四边形有限元,在任意四边形网格上得到了最优收敛阶O(h~(3/2)),这是Wilson元和类Wilson元所得不到的,这里h是趋向于0的剖分参数.  相似文献   

8.
电报方程H~1-Galerkin非协调混合有限元分析   总被引:5,自引:3,他引:2  
主要研究一类电报方程的H~1-Galerkin非协调混合有限元方法,在任意四边形网格剖分下,其逼近空间分别取为类Wilson元与双线性Q_1元,在不需要满足LBB相容性条件及不采用传统的Ritz投影的情况下,得到了与常规有限元方法相同的L~2-模和H~1-模的误差估计,进一步拓展了H~1-Galerkin混合有限元和类Wilson元的应用范围.  相似文献   

9.
具有几何对称性的12参数矩形板元   总被引:6,自引:1,他引:5  
1 引言 三角形板元中,形式最简单的是九参数元,节点参数是单元三个顶点上的函数值和两个一阶偏导数值,非协调九参三角形板元的研究取得了丰硕成果,根据不同方法已构造出多种收敛性能好的单元.相比之下,矩形板元的研究较少见报道.矩形板元中形式最简单的是12参元,节点参数是单元4个顶点上的函数值和两个一阶偏导数值,这类似于九参三角形板元.常见的12参矩形板元是ACM元,其形函数空间是完整3次多项式空间加上两个4次多项式的基函数,ACM元是C°元,但位移形函数的外法向导数平均值在单元间不连续,这类似于Zienkiewicz九参三角形板元,但由于矩形单元的特殊形状,ACM元是收敛的.龙驭球教授等在[1]中提出一种12参矩形广义协调元,其位移形函数的外法向导数平均值在  相似文献   

10.
利用分析specht元的技巧,构造了一类新的非协调四边形单元,并证明由此产生的有限元对任意四边形网格收敛且效果同Wilson元.QP6元是其中的特例  相似文献   

11.
A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1.  相似文献   

12.
This paper introduces a rather general technique for computing the average-case performance of dynamic data structures, subjected to arbitrary sequences of insert, delete, and search operations. The method allows us effectively to evaluate the integrated cost of various interesting data structure implementations, for stacks, dictionaries, symbol tables, priority queues, and linear lists; it can thus be used as a basis for measuring the efficiency of each proposed implementation. For each data type, a specific continued fraction and a family of orthogonal polynomials are associated with sequences of operations: Tchebycheff for stacks, Laguerre for dictionaries, Charlier for symbol tables, Hermite for priority queues, and Meixner for linear lists. Our main result is an explicit expression, for each of the above data types, of the generating function for integrated costs, as a linear integral transform of the generating functions for individual operation costs. We use the result to compute explicitly integrated costs of various implementations of dictionaries and priority queues.  相似文献   

13.
Vasil'eva  E. V. 《Mathematical Notes》2004,76(5-6):628-639
We obtain lower bounds for the rate of convergence of reconstruction algorithms for distributed-parameter systems of parabolic type. In the case of a pointwise constraint on control for known reconstruction algorithms, we establish a lower bound on the rate of convergence, which shows that, given certain conditions, for each solution of the system one can choose such a collection of measurements so that the reconstruction error will not be less than a certain value. In the case of unbounded controls, we obtain lower bounds for a possible reconstruction error for each trajectory as well as for a given set of trajectories. For a system of special form, we construct an algorithm for which we obtain upper and lower bounds for accuracy having identical order for a specific choice of matching of the parameters.  相似文献   

14.
弱非性理论已被广泛用于流动稳定性理论及其它领域.然而其应用对某些问题虽是成功的,但对另一些问题,其结果却常不令人满意,特别是对转捩或自由剪切流中涡的演化这类问题,这时理论研究的目的不是寻找稳态解,而是预测演化过程.在本文中,我们将研究不成功的原因并建议一些改进的办法.  相似文献   

15.
The paper is focused on high-order compact schemes for direct numerical simulation (DNS) and large eddy simulation (LES) for flow separation, transition, tip vortex, and flow control. A discussion is given for several fundamental issues such as high quality grid generation, high-order schemes for curvilinear coordinates, the CFL condition for complex geometry, and high-order weighted compact schemes for shock capturing and shock–vortex interaction. The computation examples include DNS for K-type and H-type transition, DNS for flow separation and transition around an airfoil with attack angle, control of flow separation by using pulsed jets, and LES simulation for a tip vortex behind the juncture of a wing and flat plate. The computation also shows an almost linear growth in efficiency obtained by using multiple processors.  相似文献   

16.
Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities for the mode of the GH distribution for general parameter values. As a special case, we deduce tight two-sided inequalities for the mode of the variance-gamma (VG) distribution, and through a similar approach we also obtain tight two-sided inequalities for the mode of the McKay Type I distribution. The analogous problem for the median is more challenging, but we conjecture some monotonicity results for the median of the VG and McKay Type I distributions, from we which we conjecture some tight two-sided inequalities for their medians. Numerical experiments support these conjectures and also lead us to a conjectured tight lower bound for the median of the GH distribution.  相似文献   

17.
A method for constructing algorithms solving the word and comparison problems for mapping class groups (in particular, for the braid group) is presented, and a family of one-side invariant orderings on the mapping class group of a surface with boundary is described. A method for constructing comparison algorithms for all finite orderings on the mapping class group of any surface with boundary is described, a fast and simple comparison algorithm for the Dehornoy order on the braid group is presented, examples of normal forms for braid groups are given, and algorithms for finding the forms are indicated. Bibliography: 15 titles.  相似文献   

18.
介绍了微分与差分方程机械化方法研究若干最新进展.主要结果包括: 微分、差分方程的特征列理论与算法,微分、差分方程系统的分解算法以及微分、差分方程解析解求解算法.  相似文献   

19.
Boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations, for which complete families of particular solutions are explicitly known. The method contains various decisions which are important for its performance, such as choice of solution subspace, choice of basis for the subspace, and choice of collocation points. Using a model problem, some particular strategies for the determination of collocation points are investigated.  相似文献   

20.
许可  范江华 《应用数学》2021,34(2):506-514
本文利用例外簇方法研究非强制混合向量变分不等式的弱有效解的存在性:首先证明若混合向量变分不等式问题不存在例外簇,则混合向量变分不等式问题的弱有效解集为非空集合:利用向量值映射的渐近映射给出自反Banach空间中非强制混合向量变分不等式的弱有效解集不存在例外簇的充分条件,从而得到混合向量变分不等式问题的弱有效解的存在性结果;我们研究了当算子为余正仿射算子时,给出混合仿射向量变分不等式不存在例外簇的充分条件,得到混合仿射向量变分不等式弱有效解的存在性,给出了混合仿射向量变分不等式的弱有效解集为非空紧致集的充分条件.将Iusem等人(2019)在有限维空间中标量混合变分不等式解的存在性结果推广到自反Banach空间中混合向量变分不等式.  相似文献   

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