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Magnetic Fluid Flows in Porous Media

Chinese Physics Letters 2011年第8期28卷 198-201页

作者： LI Ming-Jun CHEN Liang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105

The seepage law under a magnetic field is obtained by up-scaling the flow at the pore scale of rigid porous media,and the macroscopic equivalent model is also *** is proved that the macroscopic mass flow depends on the macroscopic magnetic force and the gradients of pressure and of magnetic pressure,as Zahn and Rosensweig have described in their *** permeability tensor is symmetric and positive.

关键词： macroscopic Porous magnetic

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Multifractal analysis of complex networks

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Chinese Physics B 2012年第8期21卷 080504-1-080504-1-080504-11页

作者： Wang, Dan-Ling Yu, Zu-Guo Anh, V. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QC 4001 Australia School of Mathematics and Physics University of Science and Technology Beijing Beijing 10083 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions Dq of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein - protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein - protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of Dq due to changes in the parameters of the theoretical network models is also discussed. © 2012 Chinese Physical Society and IOP Publishing Ltd.

关键词： Small-world networks

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Dependence Analysis of the Solutions on the Parameters of Fractional Delay Differential Equations

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Advances in Applied Mathematics and Mechanics 2011年第5期3卷 586-597页

作者： Shuiping Yang Aiguo Xiao Xinyuan Pan School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityHunan 411105China Department of Mathematics Huizhou UniversityGuangdong 516007China

In this paper,we investigate the dependence of the solutions on the parameters(order,initial function,right-hand function)of fractional delay differential equations(FDDEs)with the Caputo fractional *** results includi... 详细信息

关键词： Fractional delay differential equation Caputo fractional derivative dependence

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A lowest order divergence-free finite element on rectangular grids

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中国数学前沿 2011年第2期6卷 253-270页

作者： Yunqing HUANG Shangyou ZHANG Department of Mathematical Sciences University of Delaware Newark DE 19716 USA Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China

It is shown that the conforming Q2,1;1,2-Q'1 mixed element is stable, and provides optimal order of approximation for the Stokes equations on rectangular grids. Here, Q2,1;1,2 = Q2,1 × Q1,2, and Q2,1 denotes the space of continuous piecewise-polynomials of degree 2 or less in the x direction but of degree 1 in the y direction. Q'1 is the space of discontinuous bilinear polynomials, with spurious modes filtered. To be precise, Q'1 is the divergence of the discrete velocity space Q2,1;1,2. Therefore, the resulting finite element solution for the velocity is divergence-free pointwise, when solving the Stokes equations. This element is the lowest order one in a family of divergence-free element, similar to the families of the Bernardi-Raugel element and the RaviartThomas element.

关键词： Mixed finite element Stokes divergence-free element quadrilateral element rectangular grid

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A Priori and a Posteriori Error Analysis of the Discontinuous Galerkin Methods for Reissner-Mindlin Plates

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 649-662页

作者： Jun Hu Yunqing Huang LMAM and School of Mathematical Sciences Peking UniversityBeijing 100871China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105HunanChina

In this paper,we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate *** derive robust a posteriori ... 详细信息

关键词： A posteriori error analysis Reissner-Mindlin plate finite element reduction integration

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A Posteriori Error Estimates of Mixed Methods for Quadratic Optimal Control Problems Governed by Parabolic Equations

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Numerical Mathematics(Theory,Methods and Applications) 2011年第4期4卷 439-458页

作者： Tianliang Hou Yanping Chen Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina

In this paper,we discuss the a posteriori error estimates of the mixed finite element method for quadratic optimal control problems governed by linear parabolic *** state and the co-state are discretized by the high order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant *** derive a posteriori error estimates for both the state and the control *** estimates,which are apparently not available in the literature,are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

关键词： A posteriori error estimates quadratic optimal control problems parabolic equations mixed finite element methods

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A LEGENDRE GALERKIN SPECTRAL METHOD FOR OPTIMAL CONTROL PROBLEMS

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Journal of Systems science & Complexity 2011年第4期24卷 663-671页

作者： Yanping CHEN Nianshi XIA Nianyu YI School of Mathematical Sciences South China Normal University Guangzhou 510631 China. The Faculty of Mathematics Chengyi College Jimei University Xiamen 361021 China. Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematicsand Computational Science Xiangtan University Xiangtan 411105 China.

This paper considers the Legendre Galerkin spectral approximation for the unconstralnea optimal control problems. The authors derive a posteriori error estimate for the spectral approximation scheme of optimal control problem. By choosing the appropriate basis functions, the stiff matrix of the discretization equations is sparse. And the authors use the Fast Legendre Transform to improve the efficiency of this method. Two numerical experiments demonstrating our theoretical results are presented.

关键词： Legendre-Galerkin optimal control spectral method.

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Mathematical simulation of Metamaterial Solar Cells

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 702-715页

作者： Jichun Li Yitung Chen Yang Liu Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China Department of Mathematical Sciences University of Nevada Las VegasLas VegasNevada 89154-4020USA Department of Mechanical Engineering University of Nevada Las VegasLas VegasNevada 89154-4027USA

In this paper,we propose several solar cell designs based on *** numerical simulations of various designs with different materials are carried *** tests show that metamaterial solar cells are quite efficient,and over ... 详细信息

关键词： Maxwell’s equations metamaterial solar cell finite element method

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Convergent Adaptive Finite Element Method Based on Centroidal Voronoi Tessellations and Superconvergence

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Communications in computational Physics 2011年第7期10卷 339-370页

作者： Yunqing Huang Hengfeng Qin Desheng Wang Qiang Du Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityHunan 411105China Department of Mechanical and Electronic Engineering School of Mechanical EngineeringXiangtan UniversityHunan 411105China Division of Mathematical Sciences School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore 637371Singapore Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA

We present a novel adaptive finite element method(AFEM)for elliptic equations which is based upon the Centroidal Voronoi Tessellation(CVT)and superconvergent gradient *** constructions of CVT and its dual Centroidal Voronoi Delaunay Triangulation(CVDT)are facilitated by a localized Lloyd iteration to produce almost equilateral two dimensional *** with finite element solutions on such high quality triangulations,superconvergent recovery methods become particularly effective so that asymptotically exact a posteriori error estimations can be *** a seamless integration of these techniques,a convergent adaptive procedure is *** demonstrated by the numerical examples,the new AFEM is capable of solving a variety of model problems and has great potential in practical applications.

关键词： Finite element methods superconvergent gradient recovery Centroidal Voronoi Tessellation adaptive methods.

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Superconvergence of Rectangular Mixed Finite Element Methods for Constrained Optimal Control Problem

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Advances in Applied Mathematics and Mechanics 2010年第1期2卷 56-75页

作者： Yanping Chen Li Dai Zuliang Lu School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdongChina Mathematics Teaching and Research Group Xiguan Foreign Language SchoolGuangzhouGuangdongChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunanChina

We investigate the superconvergence properties of the constrained quadratic elliptic optimal control problem which is solved by using rectangular mixed finite element *** use the lowest order Raviart-Thomas mixed finite element spaces to approximate the state and co-state variables and use piecewise constant functions to approximate the control *** obtain the superconvergence of O(h^(1+s))(0

关键词： Constrained optimal control problem linear elliptic equation mixed finite element methods rectangular partition superconvergence properties

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