加罚N-S方程的有限元非线性Galerkin方法

非线性Galerkin方法是对耗散型非线性发展方程的一种数值解法,其空间变量不象一般Galerkin方法那样在线性空间上离散,而是在非线性流形上离散,所得逼近解在时间变量增大时可以更快地逼近其精确解.精细的理论分析可见[1],[2]等,在有限元逼近基础上将此方法应用到Navier-Stokes方程上的工作可参见[3],[4],这些文章主要针对速度与压力同时求解的混合元情形做了讨论.本文在[4]的基础上对加罚Navier-Stokes方程的一种非线性Galerkin方法的半离散和全离散有限元逼近格式分别进行了误差估     

加罚N-S方程的有限元非线性Galerkin方法

非线性Galerkin方法是对耗散型非线性发展方程的一种数值解法,其空间变量不象一般Galerkin方法那样在线性空间上离散,而是在非线性流形上离散,所得逼近解在时间变量增大时可以更快地逼近其精确解.精细的理论分析可见[1],[2]等,在有限元逼近基础上将此方法应用到Navier-Stokes方程上的工作可参见[3],[4],这些文章主要针对速度与压力同时求解的混合元情形做了讨论.本文在[4]的基础上对加罚Navier-Stokes方程的一种非线性Galerkin方法的半离散和全离散有限元逼近格式分别进行了误差估     

求解具有混合边界条件的拟线性扩散方程的有限元方法的误差估计问题

在M.F.Wheeler的[5]中,对一类拟线性抛物型方程的F.E.M,进行了颇为深入的理论分析。但是,[5]所考虑的方程,其高阶项的系数,尚有某种局限性,以致不能应用于一般的各向异性问题;对于混合边界的情形,也未加讨论。此外,[5]中所涉及的条件也是较强的,如要求解函数u(x,t)∈c~2(Ω×[0,T])等等。 本文对实践中常常遇到的具有第三混合边界条件的一类拟线性扩散问题的F.E.M,在较[5]为弱的条件下,进行了讨论,把有关拟线性问题的误差估计问题归结为某一线性椭圆边值问题F.E.M的误差估计问题。本文的结果是[1]的推广。     

关于非线性双曲型方程全离散有限元方法的稳定性和收敛性估计

本文研究非线性双曲型方程混合问题的有限元方法.这类问题的研究,对于非线性振动、渗流力学等实际问题,在理论和实用方面均有价值.关于线性、半线性双曲方程全离散有限元方法及非线性双曲方程半离散有限元方法的收敛性研究,已有[1]—[4].     

非线性双曲型守恒方程(组)的有限元分析

关于一阶线性双曲型方程有限元方法的计算格式及误差估计,G.A.Baker已在[1]中做过分析。本文将发展这个方法考察非线性守恒方程(双曲型)的初边值问题,得到了更一般的结论。这里对非线性项的处理类似于Axelsson在[2]中关于二阶拟线性抛物型方程混合问题所提出的方法。 对于非线性双曲型守恒方程组,在一定的条件下,也能得到这个结果,这样的条件在[3]或[4]中已讨论过。     

求二维半线性椭圆问题混合元解的二重网格法

1引言求解偏微分方程的混合元方法在实际问题(如油藏和地下水的数值模拟)中有广泛的应用.与标准的有限元相比,混合元方法可以同时求解两个变量即压力和流速的近似,而且能保持问题的局部守恒性,从而得到了更好的结果(如Arnold).现已有许多文献使用混合元法求解线性的(如),拟线性的(如Milner)和非线性的(如Park)二阶椭圆问题.     

一类具有吸收边界条件的二阶非线性双曲方程的混合元法分析

1　引　　言关于二阶双曲型方程的有限元解的收敛性问题 ,目前已经有不少结果 .Dupont[1 ] 给出了一类线性双曲方程 Galerkin解的 L2 误差估计 ,Baker[2 ] 对此作了改进 ,用的是一种所谓“非标准的能量方法”.这一方法为 Cowsar,Dupont,Wheeler[3] 所采用 ,分析了一类具有吸收边界条件的线性双曲方程的混合元格式的 L2收敛性 .对于非线性双曲型问题 ,袁益让 ,王宏[4,5] 等给出了标准有限元方法的 H1 与 L2 误差估计 .本文试图把 [3]的工作更进一步研究 ,我们考虑如下非线性双曲问题 :φ(x) utt= mi,j=1 xi(aij(x) p(x,u) u xj) + mi=1…     

线性椭圆问题最低次混合有限元方法的最优最大模误差估计

本文对线性椭圆问题的最低次混合元方法提出了构造混合元空间的充分条件,并建立了新的插值算子.据此得到了混合元解,伴随向量函数及其散度的最优最大模误差估计.     

二阶椭圆方程Dirichlet边值问题混合元的超收敛

关于二阶椭圆方程Dirichlet边值问题混合元的超收敛,在正则矩形网格上,林群和林甲富在文[1]中,采用一阶Raviart-Thomas混合元空间,对有限元解经后处理后,其收敛于精确解的速度从二阶提高到四阶.本文拟将这一结果进行推广,讨论二阶椭圆方程Dirichlet边值问题的k阶Raviart-Thomas混合元的超收敛,得到了以k 3阶速度收敛于精确解的有限元解.     

关于带间断非线性项的退化椭圆问题

关于带间断非线性项的椭圆问题已有不少结果,如张恭庆[8],张恭庆、姜伯驹[9],K.C.Chang[10]、[11],J,Rauch[12].他们大多使用度数理论与变分方法.我们从 F.E.Browder[1]出发,借助集值映象的变分不等式考察了一类带间断非线性项的退化椭圆问题,得到了一个存在性结论。设 X 为自反 Banach 空间,X(?)为其对偶空间,X 与 X~(?) 之间的对偶积表为〈v~(?),v〉.如果 S(?)X,(?)∈X,则记 S+(?)={s+(?)|s∈S}.     

Multidimensional first and second order symmetric Strang splitting for hyperbolic systems

We propose an algebraic basis for symmetric Strang splitting for first and second order accurate schemes for hyperbolic systems in N dimensions. Examples are given for two and three dimensions. Optimal stability is shown for symmetric systems. Lack of strong stability is shown for a non-symmetric example. Some numerical examples are presented for some Euler-like constant coefficient problems.     

Half Space and Quarter Space Dirichlet Problems for the Partial Differential Equation

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.     

Asymptotic for the cumulative distribution function of the degrees and homomorphism densities for random graphs sampled from a graphon

We give asymptotics for the cumulative distribution function (CDF) for degrees of large dense random graphs sampled from a graphon. The proof is based on precise asymptotics for binomial random variables. This result is a first step for giving a nonparametric test for identifying the degree function of a large random graph. Replacing the indicator function in the empirical CDF by a smoother function, we get general asymptotic results for functionals of homomorphism densities for partially labeled graphs. This general setting allows to recover recent results on asymptotics for homomorphism densities of sampled graphon.     

Lower Bounds for the Rate of Convergence of Dynamic Reconstruction Algorithms for Distributed-Parameter Systems

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.     

Various motivations for managerial (mis)reporting – an experimental study

In the experiment we model all possible consequences from misreporting for both the shareholder and for the manager, since we are interested in patterns in reporting behaviour resulting from different motivations for potential misrepresentation. This allows for examining the stability of the (mis)reporting behaviour in different treatments. Agents are primarily driven by the consequences for themselves rather than by the consequences for the principal, while deciding on misreporting. Participants are willing to sacrifice a small gain for themselves in order to prevent a greater loss for the principal. If agents misreport, they do it in order to generate positive rather than negative consequences for themselves. Reports in favour of the principal, but fruitless or even costly for the agent are very rare. The experiment indicates also that pro-social agents report more truthfully than pro-self agents.     

Reduced order observer design for discrete-time nonlinear systems

This work is a geometric study of reduced order observer design for discrete-time nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable discrete-time nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for discrete-time nonlinear systems using the center manifold theory for maps. We illustrate our reduced order observer construction for discrete-time nonlinear systems with an example.     

Reduced order observer design for nonlinear systems

This work is a geometric study of reduced order observer design for nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for nonlinear systems using the center manifold theory for flows. We illustrate our reduced order observer construction for nonlinear systems with a physical example, namely a nonlinear pendulum without friction.     

‘Strong’-‘weak’ precedence in scheduling: Extensions to series-parallel orders

We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series-parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) [5]. Moreover, for series-parallel posets we establish new computational complexity results for strong precedence constraints for single- and multi-machine problems.     

Sequence of operations analysis for dynamic data structures

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.     

非强制混合向量变分不等式解的存在性研究

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...