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1.
用混合有限元方法讨论稳态热传导问题的均匀化方程.给出了一种矩形剖分下的混合元格式,该格式具有各向异性特征,即剖分不满足正则性条件时也收敛,应用各向异性插值定理给出了误差分析.  相似文献   

2.
九参数广义协调元的收敛性   总被引:11,自引:4,他引:11  
石钟慈  陈绍春 《计算数学》1991,13(2):193-203
众知周所,解板弯曲问题的Zienkiewicz不协调三次元只对特殊的单元剖分才收敛.但由于这种元采用单元顶点的函数值及二个一阶导数值作为节点参数,计算简单,总体自由度少,所以相继出现一些对Zienkiewicz元的改进形式,使之对任意剖分均收敛,如拟协调元,TRUNC元,Specht元.对这些元的分析见[7—9].最近龙  相似文献   

3.
本文利用具有最优插值逼近的界面棱边元来逼近太阳系界面动态磁场问题,采用界面对齐的三角剖分对区域进行划分且跳转接口被δ-带包围.利用界面棱边元的性质,得到了关于动态磁场的最优误差估计,收敛结果为O(τ+h),其中τ和h分别是时间和空间方向的剖分步长.最后,对太阳系界面模型的动态磁场进行了数值模拟.  相似文献   

4.
本文讨论了抛物方程的基于三角形剖分和BB型对偶剖分的有限体积元法,给出了半离散及全离散有限体积元格式的最佳阶L2和H1误差估计.  相似文献   

5.
本文考虑分离图和树的平方图上团剖分问题的复杂性.文中的图均为无向简单图,团是指完备子图.分离图是指其点集可剖分为一个团和一个独立集之并的图.图 G 的团剖分是一组边不相重的团,它们包含了 G 的每条边.成员最少的团剖分叫做最小团部分.这个最小成员数叫做团剖分数,记为 CP(G).图的团剖分问题是 NP—完全的.本文的一个结果是证明了分离图上的团剖分问题仍保持,NP—完全性.  相似文献   

6.
于绍慧  郑小宏 《经济数学》2006,23(3):311-314
在求解非凸规划的分枝定界法中,剖分区间的选取直接影响到整个算法的收敛速度.本文对现有的LDB区间剖分法进行了改进,给出了一种剖分区间的选取原则,理论分析和数值算例表明采用新的ILDB算法会具有更快的收敛速度.  相似文献   

7.
我们构造了关于 R~n 的一种新的三角剖分——D_1三角剖分,且证明了它比熟知的三角剖分的单纯形个数都少.基于 D_1三角剖分,我们建立了一种新的变维数单纯算法.几个数值例子表明新的 D_1三角剖分及算法的确是更有效的.  相似文献   

8.
带组约束可靠性网络最优化问题的精确算法   总被引:1,自引:0,他引:1  
本文提出了一种求解带组约束串-并网络系统最优冗余问题的精确算法.该算法利用拉格朗日松驰和Dantzig-Wolfe分解法得到问题的上界,并结合动态规划求解子问题.算法采用一种有效的切割和剖分方法,以逐步缩小对偶间隙和保证收敛性.数值结果表明该算法对于求解带组约束可靠性最优化问题是很有效的.  相似文献   

9.
用有限条直线对区域 D进行的剖分称为贯穿剖分 ,形成剖分的直线称为贯穿线 .称始于内网点终止于 D的边界的线段为 D内的射线 ,如果一个剖分中的每一条网线或者是贯穿线的一部分或者是某一射线的一部分 ,则称该剖分为拟贯穿剖分 .由于贯穿剖分具有的特殊优越性 ,使其成为多元样条中最常用的剖分 .在多元样条里应用最广的均匀 1-型均匀 2 -型剖分就是贯穿剖分的特例 .但是 ,目前对贯穿剖分的性质研究较少 ,这限制了贯穿剖分优越性的进一步挖掘 .针对这一问题本文研究的贯穿剖分的多种性质 ,如 :边缘点的存在性 ,特型剖分域的存在性 ,染色定…  相似文献   

10.
本文在任意三角剖分△的一种特定的加细剖分△~*下,给出了S_2~1(△~*)中B-样条的一种构造方法,所得结果既可用于构造有限元法中的协调元,又可很方便地用于散乱数据的插值与拟合。本文对有关误差估计也作了分析。  相似文献   

11.
This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1(k 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k + 1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.  相似文献   

12.
The time‐dependent Stokes problem is solved using continuous, piecewise linear finite elements and a classical stabilization procedure. Four order‐one methods are proposed for the time discretization. The first one is nothing but the Euler backward scheme and requires a large linear system involving the velocity and pressure unknowns to be solved. The other three schemes allow velocity and pressure computations to be decoupled, namely the pressure‐matrix method, a method based on an inexact LU factorization, and an operator splitting method. Stability and condition number estimates are derived. Numerical experiments in two space dimensions confirm the theoretical predictions. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:632–656, 2001  相似文献   

13.
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.  相似文献   

14.
A piecewise linearization method based on the Taylor series expansion of the nonlinearities and forcing with respect to time, displacement and velocity for the study of smooth single degree-of-freedom problems, is presented. The method provides piecewise analytical solutions which are smooth everywhere, is second-order accurate in time and yields explicit finite difference formulae for the displacement and velocity. The method is applied to nine single degree-of-freedom problems and its accuracy is assessed in terms of the displacement, velocity and energy as functions of the time step, and its results are compared with those of piecewise linearization methods that use Taylor series expansion of the forcing and nonlinearities with respect to time. It is shown that, for nonlinear problems with unknown free frequency and damping, the linearization method presented here is more accurate and robust than linearization techniques based on Taylor series expansions with respect to time. For linear problems with oscillatory forcing, linearization methods that employ fourth-order expansions in time are more accurate than the linearization method proposed here provided that the time step is sufficiently small.  相似文献   

15.
本文发展Stokes问题的一个四变量杂交-混合变分方程:应力-速度-压力-拉格朗日乘子.然后发展其有限元方法:对应四变量分别用间断型Raviart—Thomas最低阶元,分片常数元,连续线性元和连续线性元的迹空间.我们获得了稳定性和最优误差界.通过后处理办法,我们得到一个适合于计算的速度-压力格式,该格式可视为“Mini”元方法的一个变形(本文格式中引入了局部投影算子).然而,本文格式关于压力具有“超收敛”结果:得到了压力关于H^1-范的误差界O(h).  相似文献   

16.
There are many papers in which approximate solution of Navier-Stokes problem is discussed by finite element method. Their error estimates are optimal, but degree of piecewise polynomials for pressure p or degree of piecewise polynomials for velocity u are not the lowest. In this papre a new element is given. Its degre for p and degree for u are the lowest and error estimates are optimal.  相似文献   

17.
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H^1 norm error estimates are given.  相似文献   

18.
In this paper, we present and analyze a finite volume method based on the Crouzeix–Raviart element for the coupled fracture model, where the fluid flow is governed by Darcy's law in the one‐dimensional fracture and two‐dimensional surrounding matrix. In the numerical scheme, the pressure in the matrix and fracture is respectively approximated by the Crouzeix–Raviart elements and piecewise constant functions, and then the velocity is calculated by piecewise constant functions element by element. The existence and uniqueness of the numerical solution are discussed, and optimal order error estimates for both the pressure p and the velocity u are proved on general triangulations. We finally carry out numerical experiments, and results confirm our theoretical analysis.  相似文献   

19.
The goal of this paper is to introduce a simple finite element method to solve the Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the method is accurate.  相似文献   

20.
In this article, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints. A priori error estimates of optimal order are derived for velocity and pressure in the energy norm and the L2-norm, respectively. Moreover, a reliable and efficient a posteriori error estimator is derived. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. In particular, we consider the abstract results with suitable stable pairs of velocity and pressure spaces like as the lowest-order Crouzeix–Raviart finite element and piecewise constant spaces, piecewise linear and constant finite element spaces. The theoretical results are illustrated by the numerical experiments.  相似文献   

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