共查询到20条相似文献,搜索用时 140 毫秒
1.
<正> 本文的目的是体现临界点定理和映象度理论的结合.利用 Leray-Schauder 映象度,本文把 A.Castro 的临界点定理([3],[4])作了推广,该定理是本文定理1中映象度=(-1)~k 的特殊情况.定理2是定理1的一个应用.作为定理2的应用,我们举出常微分方程两点边值问题解的存在性的例子.以前的结果(例如[1—4])不能证明这问题解的存在性. 相似文献
2.
§1 . IntroductionTheclassicalelastictheorydealswithacurveinR2 orR3 whichisacriticalpointforthetotalsquaredcurvaturefunctionalonregularcurveswithfixedlengthsatisfyinggivenboundaryconditions.ThiscouldtracebacktoDanielBernoulli( [1]) .Duringrecenttwodecades,severalauthors( [2 ],[3],[4 ])consideredthegeneralizationsoftheelasticatothespaceforms.ThispaperdealswiththeaffinestarlikecurvesinR2 .Westudythecriticalpointforthetotalpolynomialsubaffinecurvaturefunctionalonthosestarlikecurvessatisfyingg… 相似文献
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§ 1. Introduction ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon … 相似文献
4.
张阳 《高等学校计算数学学报》2007,29(2):157-165
1引言有限体积法是由Baliga和Patankar提出的一种数值求解偏微分方程,特别是物理学中保持守恒律方程的有效方法.由于其运用原方程的体积积分公式和有限控制体积来离散方程.使方程在控制体积上保持守恒律这一重要的物理特性,自出现以来,有了很大的发展([2-4],[10]).特征线方法([1],[8],[9])则是一种非常适合求解对流占优扩散方程的数值 相似文献
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盛平兴 《应用数学与计算数学学报》1993,7(1):94-96
1.引言我们考虑简单、局部晶体增长模型,在能控制的近似意义下,分析了实际问题中某些猜想。目前国际上讨论的大多数模型是和最简单的几何模型有关(参见Kessler,Koplik和Levine 1985[7],[8])。在Ben-Jacob,Goldenfeld,Langer和Schon([2],[3])的边界层模型中,许多结论被独立地发现。晶体增长的模型可写成如下形式: 相似文献
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赵静辉 《数学物理学报(B辑英文版)》1997,(4)
1IntroductionSincetheapproximationaboutpositivelinearoperatorscanbenaturallyinterpretedasthecorrespondingtopicsinprobabilitytheoryswecanuseprobabilitymethodtoconstructorsolvetherelatedproblem([1],[2]).Meanwhile,thetechniquesandidealsusedinapproximationtheorycanbeusedtodealwithsomequestionsinprobabilitytheory,especiallytodiscussthelimittheoryandtoestimatetheconvergentrates.Recently,M.WebastudiedthecentrallimittheorybyusingKorovkintheoryinapproximationtheory([1],[2]).Correspondingtoclassofgene… 相似文献
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<正> 本文的作者之一曾经研究过那种齐性射影及非欧几何,其中点的坐标先假定是方阵([1],[2]及其它),而从来又假定是长方阵([3],[4]及其它).另一作者则将齐性方阵几何应用于多维实射影几何及非欧几何([5],[6]).在1956年六月到七月之间作者们在 相似文献
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吴启光 《高等学校计算数学学报》1988,(2)
众所周知,热传导问题是一个典型的数学物理问题,在偏微分方程数值解法的许多著作(如[1],[2],[3],[4])中,均以热传导方程作为典型问题分析各种差分格式的收敛性和稳定性,然而一般均考虑第一类边界条件,关于热传导方程Neumann问题的稳定性的讨论却所见甚少。 相似文献
10.
§1 引论给定曲指数族 q(x,μ),Amari 在给定辅助统计量(Ancillary)的情况下研究了参数μ的一阶有效相合估计量的条件期望和条件方差.但人们有时只对参数μ的一部分 u 感兴趣,其余部分 v 视为多余参数.这时估计量可以划分为.本文根据Amari([1],[2],[3])介绍的微分几何和 Edgewerth 展开的方法研究了估计量的条件分 相似文献
11.
Shao-chunChen Yong-chengZhao Dong-yangShi 《计算数学(英文版)》2005,23(2):185-198
In this paper we give a convergence theorem for non C^0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and a twelve parameter rectangular element both with double set parameters, are presented. The convergence and numerical results of the two elements are given. 相似文献
12.
1.IntroductionShiZhongci[']hasshownthattheWilsonelementonarbitraryquadrilateralmesheswasconvergelltunderacertainconditionwithoutmodificationsofthevariationalformulation.P.LesaintandM.Zlamal[2]gaveamathematicalanalysisoftheconvergenceofthemodifiedWilsonelemeflt.Withtheseideas,thispapergivestwosimplevariationalformulationsforthequadrilateralWilsonelementandshowstheirconvergencewiththenewvariationalformulations.Usingthenewvariationalformulations,wecanreduceourcomputationalcostsbecausetwotermsa… 相似文献
13.
In this paper,a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure.The convergence analysis is presented and optimal error estimates of both broken H1-norm and L2-norm for velocity as well as the L2-norm for the pressure are derived. 相似文献
14.
The convexified Landau-Lifshitz minimisation problem in micromagnetics leads to a degenerate variational problem. Therefore strong convergence of finite element approximations cannot be expected in general. This paper introduces a stabilised finite element discretisation which allows for the strong convergence of the discrete magnetisation fields with reduced convergence order for a uniaxial model problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
《数学季刊》2017,(1)
In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H~1-norm and L~2-norm for velocity as well as the L~2-norm for the pressure are derived. 相似文献
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In this paper, we are concerned with mortar edge element methods for solving three-dimensional Maxwell's equations. A new type of Lagrange multiplier space is introduced to impose the weak continuity of the tangential components of the edge element solutions across the interfaces between neighboring subdomains. The mortar edge element method is shown to have nearly optimal convergence under some natural regularity assumptions when nested triangulations are assumed on the interfaces. A generalized edge element interpolation is introduced which plays a crucial role in establishing the nearly optimal convergence. The theoretically predicted convergence is confirmed by numerical experiments.
18.
Lin Mu Junping Wang Xiu Ye 《Numerical Methods for Partial Differential Equations》2014,30(3):1003-1029
A new weak Galerkin (WG) finite element method is introduced and analyzed in this article for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on general finite element partitions consisting of polygons or polyhedra of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter‐free. Optimal order error estimates in a discrete H2 norm is established for the corresponding WG finite element solutions. Error estimates in the usual L2 norm are also derived, yielding a suboptimal order of convergence for the lowest order element and an optimal order of convergence for all high order of elements. Numerical results are presented to confirm the theory of convergence under suitable regularity assumptions. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1003–1029, 2014 相似文献
19.
The accuracy of standard boundary element methods for elliptic boundary value problems deteriorates if the boundary of the domain contains corners or if the boundary conditions change along the boundary. Here we first investigate the convergence behaviour of standard spline Galerkin approximation on quasi-uniform meshes for boundary integral equations on polygonal domains. It turns out, that the order of convergence depends on some constant describing the singular behaviour of solutions near corner points of the boundary. In order to recover the full order of convergence for the Galerkin approximation we propose the dual singular function method which is often used for improving the accuracy of finite element methods. The theoretical convergence results are confirmed and illustrated by a numerical example. 相似文献
20.
An adaptive nonconforming finite element method is developed and analyzed that provides an error reduction due to the refinement
process and thus guarantees convergence of the nonconforming finite element approximations. The analysis is carried out for
the lowest order Crouzeix-Raviart elements and leads to the linear convergence of an appropriate adaptive nonconforming finite
element algorithm with respect to the number of refinement levels. Important tools in the convergence proof are a discrete
local efficiency and a quasi-orthogonality property. The proof does neither require regularity of the solution nor uses duality
arguments. As a consequence on the data control, no particular mesh design has to be monitored.
Supported by the DFG Research Center MATHEON ``Mathematics for key technologies' in Berlin. 相似文献