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

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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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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A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第1期15卷 68-90页

作者： Guanrong Li Yanping Chen Yunqing Huang School of Mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048GuangdongP.R.China School of Mathematical Science South China Normal UniversityGuangzhou 510631GuangdongP.R.China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanP.R.China

In this paper,a robust modified weak Galerkin(MWG)finite element method for reaction-diffusion equations is proposed and *** advantage of this method is that it can deal with the singularly perturbed reaction-diffusion *** advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries *** is worth pointing out that,in our method,the test functions space is the same as the finite element space,which is helpful for the error *** error estimates are established for the corresponding numerical approximation in various *** numerical results are reported to confirm the theory.

关键词： Reaction-diffusion equations singular perturbation modified weak Galerkin finite element methods discrete gradient

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Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1440-1458页

作者： Xingfa Yang Yin Yang Yanping Chen Jie Liu State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangsha 410082HunanChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Center for Research on Leading Technology of Special Equipment School of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou 510006GuangdongChina

In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo *** the properties of the Caputo derivative,we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel,then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra *** provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.

关键词： Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative

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Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1506-1524页

作者： Xiong Liu Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Statistics Lingnan Normal UniversityZhanjiangGuangdong 524048China

In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular *** first change the equation into an equivalent VIE so that the solution of the new equation possesses better *** integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation *** convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials,approximation theory for orthogonal polynomials,and the operator *** spectral rate of convergence for the proposed method is established in the L^(∞)-norm and weighted L^(2)-*** results are presented to demonstrate the effectiveness of the proposed method.

关键词： Chebyshev collocation method Volterra integral equations spectral rate of convergence H¨older continuity

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Efficient Synthesis of Isoquinolines by AgNO3-Catalyzed Sequential Imination-Annulation of 2-Alkynyl Aldehydes with Ammonium Bicarbonate

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Chinese Journal of Chemistry 2016年第9期34卷 857-860页

作者： Yunhui Zhao Mingjian Luo Yubo Li Xiong Liu Zilong Tang Keqin Deng Gang Zhao Hunan Province College Key Laboratory of QSAR/QSPR School of Chemistry and Chemical Engineering Hunan University of Science and Technology Xiangtan Hunan 411201 China Key Laboratory of Synthetic Chemistry of Natural Substances Shanghai Institute of Organic Chemistry Chinese Academy of Sciences Shanghai 200032 China Key Laboratory of Theoretical Chemistry and Molecular Simulation Ministry of Education Xiangtan Hunan 411201 China

An operationally simple approach for the tandem synthesis of isoquinolines by the reaction of o-alkynylalde- hydes with ammonium bicarbonate via Ag-catalyzed 6-endo-dig ring closure is described. The reaction conditions and the scope of the reaction are examined, and a variety of substituted isoquinolines are prepared in moderate to excellent yields.

关键词： isoquinolines annulation imination silver nitrate o-alkynyl aldehydes

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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

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Advances in Applied Mathematics and Mechanics 2023年第6期15卷 1631-1654页

作者： Jiaqi Zhang Yin Yang Zhaojie Zhou School of Mathematics and Computational Science Xiangtan UniversityHunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing and Information Processing of Ministry of EducationXiangtan 411105HunanChina School of Mathematics and Computational Science Xiangtan UniversityNational Center for Applied Mathematics in HunanHunan International Scientific and Technological Innovation Cooperation Base of Computational ScienceXiangtan 411105HunanChina School of Mathematics and Statistics Shandong Normal UniversityJinan 250014ShandongChina

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is *** deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is *** first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is *** experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

关键词： Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials

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RECOVERY A POSTERIORI ERROR ESTIMATES FOR GENERAL CONVEX ELLIPTIC OPTIMAL CONTROL PROBLEMS SUBJECT TO POINTWISE CONTROL CONSTRAINTS

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Journal of computational Mathematics 2009年第4期27卷 543-560页

作者： Yanping Chen Yao Fu Huanwen Liu Yongquan Dai Huayi Wei School of Mathematical Sciences South China Normal University Guangzhou 510631 China College of Mechanical Engineering Jiangxi Yu Zhou Scientific and Technological Institute Xinyu 338029 China School of Mathematics and Computer Science Guangxi University for Nationalities Nanning 530006 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University

Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.

关键词： General convex optimal control problems Finite element approximation Control constraints Superconvergence Recovery operator.

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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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Recent progress in quantifying substituent effects

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science China Chemistry 2013年第7期56卷 883-910页

作者： CAO ChenZhong WU YaXin Key Laboratory of Theoretical Chemistry and Molecular Simulation of Ministry of Education Key Laboratory of QSAR/QSPR of Hunan Provincial University School of Chemistry and Chemical Engineering Hunan University of Science and Technology School of Chemistry and Chemical Engineering University of South China

This paper summarizes significant progress in quantifying organic substituent effects in the last 20 years. The main content is as follows：（1） The principle of electronegativity equalization has gained wide acceptance, and has been used to calculate the intramolecular charge distribution and inductive effect of groups. A valence electrons equalization method was proposed to compute the molecular electronegativity on the basis of geometric mean method, harmonic mean method, and weighted mean method. This new calculation method further extended the application of the principle of electronegativity equalization. （2） A scale method was established for experimentally determining the electrophilic and nucleophilic ability of reagents, in which benzhydryliumions and quinone methides were taken as the reference compounds, and the research field was extended to the gas phase conditions, organometallic reaction and radicals system. Moreover, the nucleophilicity parameters N and electro- philicity parameters E for a series of reagents were obtained. The definition and quantitative expression of electrophilicity in- dex co and nucleophilicity index co were proposed theoretically, and the correlation between the parameters from experimental determination and the indexes from theoretical calculation was also investigated. （3） The polarizability effect parameter was initially calculated by empirical method and further developed by quantum chemistry method. Recently, the polarizability ef- fect index of alkyl （PEI） and groups （PEIx） were proposed by statistical method, and got wide applications in explaining and estimating gas-phase acidity and basicity, ionization energy, enthalpy of formation, bond energy, reaction rate, water solubility and chromatographic retention for organic compounds. （4） The excited-state substituent constant Crcc obtained directly from the UV absorption energy data of substituted benzenes, is different from the polar constants in molecular ground state an

关键词： substituent effect electronic effect steric effect molecular equalized electronegativity electrophilicity index nucleo-philicity index polarizability effect parameter excited-state substituent constant steric shielding effect

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