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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))(01.for the control ***,we present two numerical examples to confirm our superconvergence results.

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

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High time resolution observation and statistical analysis of atmospheric light extinction properties and the chemical speciation of fine particulates

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science China Chemistry 2010年第8期53卷 1801-1808页

作者： YAO TingTing1.HUANG XiaoFeng1.HE LingYan1.HU Min2,SUN TianLe1.XUE Lian1.LIN Yun1.ZENG LiWu1.& ZHANG YuanHang2 1.0} {1. for Urban Habitat Environmental science and Technology,School of Environment and Energy,Peking University Shenzhen Graduate School,Shenzhen 51.055,China 2State key Joint {1. of Environmental simulation and Pollution Control College of Environmental sciences and engineering,Peking University,Beijing 1.0871.China 1. Key Laboratory for Urban Habitat Environmental Science and Technology School of Environment and Energy Peking University Shenzhen Graduate School Shenzhen 518055 China2. State Key Joint Laboratory of Environmental Simulation and Pollution Control College of Environmental Sciences and Engineering Peking University Beijing 100871 China

In recent years,the visibility deterioration caused by regional fine particulate pollution becomes one of the crucial air pollution problems in the urban areas of our *** rapid variation of visibility and fine particulates make it difficult to estimate the relationship between them precisely and accurately unless high time resolution observation data can be *** study aims to fill this gap in the field of atmospheric science by establishing a formula using multiple linear *** fitting goodness (R2=0.91.,n=31.7) was obtained using 1. min average of high-resolution real-time light scattering coefficients,light absorption coefficients,main chemical speciation concentration in PM1.and some meteorological parameters from 1. Jan to 1. Feb,*** shows that the average light extinction coefficient during the observation in the winter of Shenzhen was measured to be 290 ± 1.3 Mm?1.consisting of 72% of light scattering and 21. of *** terms of the percentage contribution of PM1.chemical species to the total light extinction,the organic matter was estimated to be most with an average of 45%,followed by ammonium sulfate with an average of 24%.The contributions of black carbon and ammonium nitrate were 1.% and 1.%,***,the diurnal variation of light extinction was investigated as well in this study.

关键词： light extinction PM1 chemical speciation high time resolution multiple linear regressions

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Heterogeneous reaction of NO_2 with sea salt particles

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science China Chemistry 2010年第12期53卷 2652-2656页

作者： YE ChunXiang 1.LI HongJun 1.ZHU Tong 1.SHANG Jing 1.ZHANG ZeFeng 1.2 & ZHAO DeFeng 1.1.State key Joint {1. of Environmental simulation and Pollution Control College of Environmental sciences and engineering,Peking University,Beijing 1.0871.China 2 College of Atmospheric Physics,Nanjing University of Information science and Technology,Nanjing 21.044,China 1. State Key Joint Laboratory of Environmental Simulation and Pollution Control College of Environmental Sciences and Engineering Peking University Beijing 100871 China2. College of Atmospheric Physics Nanjing University of Information Science and Technology Nanjing 210044 China

To understand how NO2 reacts with sea salt particles in the atmosphere of Mega-cities in coastal zones,the heterogeneous reaction of NO2 on the surface of wet sea salt was investigated with diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and ion chromatography (IC).Kinetic measurements indicated that nitrate formation on sea salt was second order in NO 2 concentration and reactive uptake coefficients were (5.51.± 0.1.) × 1.-7 and 1.26 × 1.-6 respectively under 0% and 20% relative humidity (RH) at NO 2 molecular concentration of 1.96 × 1.1. mol/*** results showed that liquid water was formed at the site of MgCl2·6H2O,CaCl2·2H2O on the surface of sea salt and made the reaction more sustainable by releasing hydrated water and absorbing water from air even under a low RH (30%).Therefore,pure NaCl particles should not be used to represent sea salt in studies of the heterogeneous reaction with NO2.

关键词： sea salt particles diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) hydrated water absorbed water reactive uptake coefficient

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Level Set interface treatment and its application in Euler method

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science China(Physics,Mechanics & Astronomy) 2010年第2期53卷 227-236页

作者： WU KaiTeng1.2,HAO Li3,WANG Cheng4 & ZHANG Li1.2 1.Numerical simulation Sichuan Higher School {1. laboratory,Neijiang Normal University,Neijiang 641.1.,China 2 College of Mathematics and Information science,Neijiang Normal University,Neijiang 641.1.,China 3 College of science,Beijing University of Civil engineering and Architecture,Beijing 1.0044,China 4 State {1. laboratory of Explosion science and Technology,Beijing Institute of Technology,Beijing 1.0081.China 1. Numerical Simulation Sichuan Higher School Key Laboratory Neijiang Normal University Neijiang 641112 China2. College of Mathematics and Information Science Neijiang Normal University Neijiang 641112 China3. College of Science Beijing University of Civil Engineering and Architecture Beijing 100044 China4. State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China

Level Set interface treatment method is introduced into Euler method,which is employed for interface treatment method for multi-materials. Combined with the ghost fluid method,the moving interface is tracked. Fifth-order WENO spatial discretization and third-order TVD Runge-Kutta time discretization methods are used. Shock-wave action on bubble,implosion and velocity field Shock effect bubbles; implosion and velocity field are simulated by means of LS-MMIC3D programmed by C++. Nu-merical results show that the Level Set interface treatment method is effective and feasible for multi-material interface treatment in comparison with the WENO method.

关键词： Euler method Level Set method shock-wave action on bubble implosion numerical simulation

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Identification of secondary organic aerosols based on aerosol mass spectrometry

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science China Chemistry 2010年第12期53卷 2593-2599页

作者： HUANG XiaoFeng 1.ZHAO QianBiao 1.2,HE LingYan 1.HU Min 2,BIAN QiJing 3,XUE Lian 1.& ZHANG YuanHang 2 1.key {1. for Urban Habitat Environmental science and Technology School of Environment and Energy,Peking University Shenzhen Graduate School,Shenzhen 51.055,China 2 State key Joint {1. of Environmental simulation and Pollution Control College of Environmental sciences and engineering,Peking University,Beijing 1.0871.China 3 Division of Environment,Hong Kong University of science & Technology,Hong Kong,China 1. Key Laboratory for Urban Habitat Environmental Science and Technology School of Environment and Energy Peking University Shenzhen Graduate School Shenzhen 518055 China2. State Key Joint Laboratory of Environmental Simulation and Pollution Control College of Environmental Sciences and Engineering Peking University Beijing 100871 China3. Division of Environment Hong Kong University of Science & Technology Hong Kong China

Secondary organic aerosol (SOA) is one of the major components of aerosols in the atmosphere and has not been well understood so *** to the complex chemical composition of organic aerosols,the identification of SOA has been a hotspot and difficult issue in the field of aerosol *** study attempts to quantitatively identify SOA in winter of Shenzhen based on positive matrix factorization (PMF) *** sources were resolved and SOA was identified subsequently according to the characteristic ion fragments measured by highly time-resolved aerosol mass spectrometer *** showed that in the winter of Shenzhen the average SOA concentration was 9.41.6.33 g/m 3,accounting for 39.9±21.8% of the total organic *** with primary organic aerosol (POA),the SOA concentrations had no large variation,suggestive of characteristics of regional secondary *** ratio of SOA/BC had pronounced diurnal variation,similar to that of O x (O3+NO2),indicating SOA formation was significantly controlled by activity of photochemistry in the *** most effective period for SOA formation was from 9 am～3 pm since the SOA/BC ratio increased by 1.2% during this *** study provides a new technical method and a new idea for SOA investigation.

关键词： secondary organic aerosol aerosol mass spectrometry positive matrix factorization (PMF)

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AN EFFICIENT MOVING MESH METHOD FOR A MODEL OF TURBULENT FLOW IN CIRCULAR TUBES

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Journal of computational Mathematics 2009年第2期27卷 388-399页

作者： Yin Yang Yanping Chen Yunqing Huang Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China School of Mathematical Sciences South China Normal University Guangzhou China

This paper presents an efficient moving problem with an optimal control constrained mesh method to solve a nonlinear singular condition. The physical problem is governed by a new model of turbulent flow in circular tubes proposed by Luo et al. using Prandtl＇s mixing-length theory. Our algorithm is formed by an outer iterative algorithm for handling the optimal control condition and an inner adaptive mesh redistribution algorithm for solving the singular governing equations. We discretize the nonlinear problem by using a upwinding approach, and the resulting nonlinear equations are solved by using the Newton- Raphson method. The mesh is generated and the grid points are moved by using the arc-length equidistribution principle. The numerical results demonstrate that proposed algorithm is effective in capturing the boundary layers associated with the turbulent model.

关键词： Eddy viscosity Turbulent pipe flow Boundary layer Optimal control Moving mesh

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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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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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A Posteriori Error Estimates of Triangular Mixed Finite Element Methods for Semilinear Optimal Control Problems

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Advances in Applied Mathematics and Mechanics 2009年第2期1卷 242-256页

作者： Zuliang Lu Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtan 411105HunanP.R.China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongP.R.China

In this paper,we present an a posteriori error estimates of semilinear quadratic constrained optimal control problems using triangular mixed finite element *** state and co-state are approximated by the order k≤1.RaviartThomas mixed finite element spaces and the control is approximated by piecewise constant *** derive a posteriori error estimates for the coupled state and control approximations.A numerical example is presented in confirmation of the theory.

关键词： Semilinear optimal control problems mixed finite element methods a posteriori error estimates

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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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