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991.
This paper considers numerical simulation of time‐dependent non‐linear partial differential equation resulting from a single non‐linear conservation law in h, p, k mathematical and computational framework in which k=(k1, k2) are the orders of the approximation spaces in space and time yielding global differentiability of orders (k1?1) and (k2?1) in space and time (hence k‐version of finite element method) using space–time marching process. Time‐dependent viscous Burgers equation is used as a specific model problem that has physical mechanism for viscous dissipation and its theoretical solutions are analytic. The inviscid form, on the other hand, assumes zero viscosity and as a consequence its solutions are non‐analytic as well as non‐unique (Russ. Math. Surv. 1962; 17 (3):145–146; Russ. Math. Surv. 1960; 15 (6):53–111). In references (Russ. Math. Surv. 1962; 17 (3):145–146; Russ. Math. Surv. 1960; 15 (6):53–111) authors demonstrated that the solutions of inviscid Burgers equations can only be approached within a limiting process in which viscosity approaches zero. Many approaches based on artificial viscosity have been published to accomplish this including more recent work on H(Div) least‐squares approach (Commun. Pure Appl. Math. 1965; 18 :697–715) in which artificial viscosity is a function of spatial discretization, which diminishes with progressively refined discretizations. The thrust of the present work is to point out that: (1) viscous form of the Burgers equation already has the essential mechanism of viscosity (which is physical), (2) with progressively increasing Reynolds (Re) number (thereby progressively reduced viscosity) the solutions approach that of the inviscid form, (3) it is possible to compute numerical solutions for any Re number (finite) within hpk framework and space–time least‐squares processes, (4) the space–time residual functional converges monotonically and that it is possible to achieve the desired accuracy, (5) space–time, time marching processes utilizing a single space–time strip are computationally efficient. It is shown that viscous form of the Burgers equation without linearizing provides a physical and viablemechanism for approaching the solutions of inviscid form with progressively increasing Re. Numerical studies are presented and the computed solutions are compared with published work. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
992.
993.
广义Stirling数偶的理论及应用 总被引:5,自引:2,他引:3
The object of this expository paper is to sum up several results concerning generalized Stirling number (GSN) pairs investigated earlier by the author. Also expounded in some detail are two kinds of extended GSN pairs with applications (illustrative examples). 相似文献
994.
The linear stability of the linear Phan-Thien Tanner (PTT) fluid model is investigated for plane Poiseuille flow. The PTT model involves parameters that can be used to fit shear and extensional data, which makes it suitable for describing both polymer solutions and melts. The base flow is determined using a Chebyshev-tau method. The linear stability equations are also discretized using Chebyshev approximations to furnish a generalized eigenvalue problem. The spectrum is shown to comprise a continuous part and a discrete part. The theoretical and numerical results are validated for the UCM and Oldroyd-B models, which are special cases of the PTT model, by comparing with results in the literature. It is demonstrated that the linear PTT fluid is stable to infinitesimal disturbances with respect to the range of shear-thinning, extensional and elasticity parameters considered. The computational efficiency and accuracy of the numerical method are also investigated. 相似文献
995.
HUANG Jianguo SHI Zhongci & XU Yifeng Department of Mathematics Shanghai Jiaotong University Shanghai China Division of Computational Science E-lnstitute of Shanghai Universities Shanghai Normal University China Institute of Computational Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(7):986-1007
The aim of this paper is to study the static problem about a general elastic multi-structure composed of an arbitrary number of elastic bodies, plates and rods. The mathematical model is derived by the variational principle and the principle of virtual work in a vector way. The unique solvability of the resulting problem is proved by the Lax-Milgram lemma after the presentation of a generalized Korn's inequality on general elastic multi-structures. The equilibrium equations are obtained rigorously by only assuming some reasonable regularity of the solution. An important identity is also given which is essential in the finite element analysis for the problem. 相似文献
996.
997.
Peixia Gao Sabine Wittevrongel Joris Walraevens Herwig Bruneel 《Mathematical Methods of Operations Research》2008,67(2):269-284
In this paper, we study the behavior of a discrete-time multiserver buffer system with infinite buffer size. Packets arrive
at the system according to a two-state Markovian arrival process. The service times of the packets are assumed to be constant,
equal to multiple slots. The behavior of the system is analyzed by means of an analytical technique based on probability generating
functions (PGF’s). Explicit expressions are obtained for the PGF’s of the system contents and the packet delay. From these,
the mean values, the variances and the tail distributions of the system contents and the packet delay are calculated. Numerical
examples are given to show the influence of various model parameters on the system behavior. 相似文献
998.
Maria Alessandra Ragusa 《Journal of Global Optimization》2008,40(1-3):361-368
In this note we prove a sufficient condition for commutators of fractional integral operators to belong to Vanishing Morrey
spaces VL
p,λ. In doing this we use an extension on Morrey spaces of an inequality by Fefferman and Stein concerning the sharp maximal
function and the fractional maximal function and related Morrey inequalities.
相似文献
999.
Alan Noell 《Journal of Geometric Analysis》2008,18(4):1058-1087
This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been
published elsewhere.
相似文献
1000.
M. Calixto J. Guerrero J. C. Sánchez-Monreal 《Journal of Fourier Analysis and Applications》2008,14(4):538-567
Using coherent-state techniques, we prove a sampling theorem for Majorana’s (holomorphic) functions on the Riemann sphere
and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling.
Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators
through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann
sphere, with spins up to J, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established
through a discrete Bargmann transform.
相似文献