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Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems

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Numerical Mathematics(Theory,Methods and Applications) 2012年第4期5卷 573-591页

作者： Yuelong Tang Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina

This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control *** time discretization is based on the backward Euler *** state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant *** derive the superconvergence properties of finite element *** using the superconvergence results,we obtain recovery type a posteriori error *** numerical examples are presented to verify the theoretical results.

关键词： General convex optimal control problems fully discrete finite element approximation a posteriori error estimates superconvergence recovery operator

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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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Error Estimates and Superconvergence of Mixed Finite Element Methods for Optimal Control Problems with Low Regularity

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Advances in Applied Mathematics and Mechanics 2012年第6期4卷 751-768页

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

In this paper,we investigate the error estimates and superconvergence property of mixed finite element methods for elliptic optimal control *** state and co-state are approximated by the lowest order Raviart-Thomas mixed fi-nite element spaces and the control variable is approximated by piecewise constant *** derive L^(2) and L^(∞)-error estimates for the control ***,using a recovery operator,we also derive some superconvergence results for the control ***,a numerical example is given to demonstrate the theoretical results.

关键词： Elliptic equations optimal control problems superconvergence error estimates mixed finite element methods

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Superconvergence and L^(∞)-Error Estimates of RT1Mixed Methods for Semilinear Elliptic Control Problems with an Integral Constraint

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Numerical Mathematics(Theory,Methods and Applications) 2012年第3期5卷 423-446页

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

In this paper,we investigate the superconvergence property and the L∞-error estimates of mixed finite element methods for a semilinear elliptic control problem with an integral *** state and co-state are approximated by the order one Raviart-Thomas mixed finite element space and the control variable is approximated by piecewise constant functions or piecewise linear *** derive some superconvergence results for the control variable and the state variables when the control is approximated by piecewise constant ***,we derive L∞-error estimates for both the control variable and the state variables when the control is discretized by piecewise linear ***,some numerical examples are given to demonstrate the theoretical results.

关键词： Semilinear elliptic equations optimal control problems superconvergence L∞-error estimates mixed finite element methods postprocessing

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An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

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Advances in Applied Mathematics and Mechanics 2014年第2期6卷 145-164页

作者： Wei Zhu Shi Shu Lizhi Cheng School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105HunanChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105HunanChina Department of Mathematics and Computational Science College of ScienceNational University of Defense TechnologyChangsha 410073HunanChina

In this paper,we propose a fast proximity point algorithm and apply it to total variation(TV)based image *** novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation(TV)based image restoration have been *** current algorithms for TV-based image restoration,such as Chambolle’s projection algorithm,the split Bregman algorithm,the Berm´udez-Moreno algorithm,the Jia-Zhao denoising algorithm,and the fixed point algorithm,can be viewed as special cases of the new first-order ***,the convergence of the new algorithm has been analyzed at ***,we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at *** experiments illustrate the efficiency of the proposed algorithms.

关键词： Proximity point operator image restoration total variation first-order schemes.

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The parallel generation of 2-D Hilbert Space-filling Curve on GPU

The parallel generation of 2-D Hilbert Space-filling Curve o...

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2012 5th International Conference on Biomedical engineering and Informatics, BMEI 2012

作者： Feng, Chunsheng Shu, Shi Wang, Junxian Li, Zheng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (纸本)9781467311816

In this paper, we propose two parallel Hilbert Space-filling Curve(HSFC) generation algorithms BMIMp and SDDMp based on block matrix iteration method(BMIM) and state diagrams driver method(SDDM) in the CUDA parallel programming mode. Numerical results show that both of them obtain high parallel speedup. Especially, the speedup of BMIMp and SDDMp can reach 207 and 290 respectively for the 14-order HSFC. Furthermore, BMIMp outperforms SDDMp when considering the total computation time. © 2012 IEEE.

关键词： Iterative methods

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Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations

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Advances in Applied Mathematics and Mechanics 2015年第1期7卷 74-88页

作者： Yin Yang Yanping Chen Yunqing Huang Wei Yang Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China School ofMathematical Sciences South China Normal UniversityGuangzhou 510631China

A Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second *** provide a rigorous error analysis for the proposed method,which indicate that the numerical errors in L2-norm and L¥-norm will decay exponentially provided that the kernel function is sufficiently *** results are presented,which confirm the theoretical prediction of the exponential rate of convergence.

关键词： Spectral method nonlinear Volterra integral equations

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Legendre spectral Galerkin method for second-kind Volterra integral equations

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中国高等学校学术文摘·数学 2009年第1期4卷 181-193页

作者： Zhengsu WAN Yanping CHEN Yunqing HUANG Department of Mathematics Hunan Institute of Science and TechnologyYueyang 414006China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105China

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this *** provide a rigorous error analysis for the proposed method,which indicates that the numerical errors (in the L2 norm) will decay exponentially provided that the kernel function and the source function are sufficiently *** examples are given to illustrate the theoretical results.

关键词： Volterra integral equation Legendre spectral Galerkin method convergence

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Numerical Investigation on the Boundary Conditions for the Multiscale Base Functions

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Communications in computational Physics 2009年第5期5卷 928-941页

作者： Shan Jiang Yunqing Huang Department of Mathematics Xiangtan UniversityXiangtan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied MathematicsXiangtan UniversityXiangtan 411105China

We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale *** key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary *** boundary conditions are chosen to extract more accurate boundary information in the local *** consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base *** examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.

关键词： Multiscale finite element method multiscale base functions oscillatory boundary condition periodic coefficient non-periodic coefficient

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FETD Study of theWave Propagation in Chiral Metamaterials

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Advances in Applied Mathematics and Mechanics 2021年第1期13卷 191-202页

作者： Lei Yang Fuhao Liu Wei Yang Faculty of Information Technology Macao University of Science and TechnologyMacaoChina School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China Hunan Key Laboratory for Computation and Simulation in Science and Engineering and School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China

In this paper,we propose a finite element time-domain(FETD)method for the Maxwell’s equations in chiral metamaterials(CMMs).The time-domain model equations are constructed by the auxiliary differential equations(ADEs)*** source excitation method entitled total-field and scattered-field(TF/SF)decomposition technique is applied to FETD method for the first time in simulating the propagation of electromagnetic wave in CMMs,based on which a unified ADE-FETD-UPMLTF/SF scheme is proposed to simulate the wave in *** following properties of CMMs can be observed successfully from the numerical experiments based on our method,i.e.,the ability of the polarization rotation,and the negative phase *** amplitude of reflected wave can effectively be controlled by the physical parameters of CMMs.

关键词： Maxwell’s equations finite element time-domain(FETD) chiral metamaterials(CMMs).

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