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A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem
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作者 Shiying Wang Shuo Liu 《Engineering(科研)》 2024年第4期83-101,共19页
In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation o... In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results. 展开更多
关键词 Nonconforming Virtual Element Method Optimal Control Problem a Priori error Estimate
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Efficient error estimation in quantum key distribution 被引量:5
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作者 李默 Patcharapong Treeviriyanupab +3 位作者 张春梅 银振强 陈巍 韩正甫 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第1期153-156,共4页
In a quantum key distribution(QKD) system, the error rate needs to be estimated for determining the joint probability distribution between legitimate parties, and for improving the performance of key reconciliation.... In a quantum key distribution(QKD) system, the error rate needs to be estimated for determining the joint probability distribution between legitimate parties, and for improving the performance of key reconciliation. We propose an efficient error estimation scheme for QKD, which is called parity comparison method(PCM). In the proposed method, the parity of a group of sifted keys is practically analysed to estimate the quantum bit error rate instead of using the traditional key sampling. From the simulation results, the proposed method evidently improves the accuracy and decreases revealed information in most realistic application situations. 展开更多
关键词 error estimation parity comparison quantum key distribution
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An Online Model Correction Method Based on an Inverse Problem:Part I—Model Error Estimation by Iteration 被引量:3
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作者 XUE Haile SHEN Xueshun CHOU Jifan 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2015年第10期1329-1340,共12页
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the pred... Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS. 展开更多
关键词 model error past data inverse problem error estimation model correction GRAPES-GFS
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Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method 被引量:2
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作者 林治家 庄茁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第1期33-48,共16页
An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error b... An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed. 展开更多
关键词 goal-oriented error estimation finite element analysis fracture mechanics continuum-based shell
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Application of an Error Statistics Estimation Method to the PSAS Forecast Error Covariance Model 被引量:1
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作者 Runhua YANG Jing GUO Lars Peter RIISHФJGAARD 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2006年第1期33-44,共12页
In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the paralneters required by a forecast error covariance model are difficult to obtain due to the absenc... In atmospheric data assimilation systems, the forecast error covariance model is an important component. However, the paralneters required by a forecast error covariance model are difficult to obtain due to the absence of the truth. This study applies an error statistics estimation method to the Pfiysical-space Statistical Analysis System (PSAS) height-wind forecast error covariance model. This method consists of two components: the first component computes the error statistics by using the National Meteorological Center (NMC) method, which is a lagged-forecast difference approach, within the framework of the PSAS height-wind forecast error covariance model; the second obtains a calibration formula to rescale the error standard deviations provided by the NMC method. The calibration is against the error statistics estimated by using a maximum-likelihood estimation (MLE) with rawindsonde height observed-minus-forecast residuals. A complete set of formulas for estimating the error statistics and for the calibration is applied to a one-month-long dataset generated by a general circulation model of the Global Model and Assimilation Office (GMAO), NASA. There is a clear constant relationship between the error statistics estimates of the NMC-method and MLE. The final product provides a full set of 6-hour error statistics required by the PSAS height-wind forecast error covariance model over the globe. The features of these error statistics are examined and discussed. 展开更多
关键词 forecast error statistics estimation data analysis forecast error covariance model
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Energy efficiency enhancement of two-way amplifier forward relaying with channel estimation error 被引量:1
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作者 师晓晔 葛建华 +1 位作者 李靖 张沉思 《Journal of Central South University》 SCIE EI CAS 2014年第3期987-992,共6页
In order to save energy consumption of two-way amplifier forward(AF) relaying with channel estimation error, an energy efficiency enhancement scheme is proposed in this work. Firstly, through the analysis of two-way A... In order to save energy consumption of two-way amplifier forward(AF) relaying with channel estimation error, an energy efficiency enhancement scheme is proposed in this work. Firstly, through the analysis of two-way AF relaying mode with channel estimation error, the resultant instantaneous SNRs at end nodes is obtained. Then, by using a high SNR approximation, outage possibility is acquired and its simple closed-form expression is represented. Specially, for using the energy resource more efficiently, a low-complexity power allocation and transmission mode selection policy is proposed to enhance the energy efficiency of two-way AF relay system. Finally, relay priority region is identified in which cooperative diversity energy gain can be achieved. The computer simulations are presented to verify our analytical results, indicating that the proposed policy outperforms direct transmission by an energy gain of 3 dB at the relative channel estimation error less than 0.001. The results also show that the two-way AF relaying transmission loses the two-way AF relaying transmission loses its superiority to direct transmission in terms of energy efficiency when channel estimation error reaches 0.03. 展开更多
关键词 AMPLIFY-AND-FORWARD channel estimation error cooperative energy gain energy efficiency outage probability two-way relay
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PERFORMANCE OF THE ZERO FORCING PRECODING MIMO BROADCAST SYSTEMS WITH CHANNEL ESTIMATION ERRORS 被引量:1
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作者 Wang Jing Liu Zhanli Wang Yan You Xiaohu 《Journal of Electronics(China)》 2007年第4期490-495,共6页
In this paper, the effect of channel estimation errors upon the Zero Forcing (ZF) precoding Multiple Input Multiple Output Broadcast (MIMO BC) systems was studied. Based on the two kinds of Gaussian estimation error m... In this paper, the effect of channel estimation errors upon the Zero Forcing (ZF) precoding Multiple Input Multiple Output Broadcast (MIMO BC) systems was studied. Based on the two kinds of Gaussian estimation error models, the performance analysis is conducted under different power allocation strategies. Analysis and simulation show that if the covariance of channel estimation errors is independent of the received Signal to Noise Ratio (SNR), imperfect channel knowledge deteriorates the sum capacity and the Bit Error Rate (BER) performance severely. However, under the situation of orthogonal training and the Minimum Mean Square Error (MMSE) channel estimation, the sum ca- pacity and BER performance are consistent with those of the perfect Channel State Information (CSI) with only a performance degradation. 展开更多
关键词 Zero Forcing (ZF) Multiple Input Multiple Output BroadCast (MIMO BC) system Channel estimation errors Sum capacity
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Array-error estimation method for multi-channel SAR systems in azimuth 被引量:1
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作者 Lun Ma Guisheng Liao +2 位作者 Aifei Liu Yanling Jiang Ling Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第4期815-821,共7页
For multi-channel synthetic aperture radar(SAR) systems, since the minimum antenna area constraint is eliminated,wide swath and high resolution SAR image can be achieved.However, the unavoidable array errors, consis... For multi-channel synthetic aperture radar(SAR) systems, since the minimum antenna area constraint is eliminated,wide swath and high resolution SAR image can be achieved.However, the unavoidable array errors, consisting of channel gainphase mismatch and position uncertainty, significantly degrade the performance of such systems. An iteration-free method is proposed to simultaneously estimate position and gain-phase errors.In our research, the steering vectors corresponding to a pair of Doppler bins within the same range bin are studied in terms of their rotational relationships. The method is based on the fact that the rotational matrix only depends on the position errors and the frequency spacing between the paired Doppler bins but is independent of gain-phase error. Upon combining the projection matrices corresponding to the paired Doppler bins, the position errors are directly obtained in terms of extracting the rotational matrix in a least squares framework. The proposed method, when used in conjunction with the self-calibration algorithm, performs stably as well as has less computational load, compared with the conventional methods. Simulations reveal that the proposed method behaves better than the conventional methods even when the signal-to-noise ratio(SNR) is low. 展开更多
关键词 error estimation multi-channel synthetic aperture radar(SAR) system array signal processing
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Channel Error Estimation Methods Comparison under Different Conditions for Multichannel HRWS SAR Systems 被引量:1
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作者 Tingting Jin Xiaolan Qiu +1 位作者 Donghui Hu Chibiao Ding 《Journal of Computer and Communications》 2016年第3期88-94,共7页
Multichannel synthetic aperture radar (SAR) in azimuth can resolve the contradiction between high resolution and wide swath faced with traditional SAR imaging. However, channel errors will degrade the performance of i... Multichannel synthetic aperture radar (SAR) in azimuth can resolve the contradiction between high resolution and wide swath faced with traditional SAR imaging. However, channel errors will degrade the performance of imaging. This paper compares the performances of four channel error estimation algorithms under different clutter distributions and SNR conditions. Further, explanations are given for performance differences of the four algorithms, which provide evidence for method selection in engineering applications. 展开更多
关键词 Synthetic Aperture Radar (SAR) High Resolution and Wide Swath (HRWS) Multi-Channel in Azimuth Channel error estimation
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ERROR ESTIMATION OF INTERPOLATION ON PORE STRUCTURE ANALYSIS
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作者 管昌生 崔崇 陆宇萍 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 1995年第4期48-51,共4页
In this paper we computed the data of pore structure with Lagrange interpolation method, analyzed the convergence of the method and deduced the corresponding error estimation formula.
关键词 pore structure INTERPOLATION CONVERGENCE error estimation
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Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method
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作者 林治家 由小川 庄茁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第5期539-552,共14页
Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It lead... Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures. 展开更多
关键词 goal-oriented error estimation finite element method (FEM) direct-solutionsteady-state analysis frequency domain
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Systematic error real-time registration based onmodified input estimation
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作者 jianjuan xiu kai dong you he 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第5期986-992,共7页
In order to estimate the systematic error in the processof maneuvering target adaptive tracking, a new method is proposed.The proposed method is a linear tracking scheme basedon a modified input estimation approach. A... In order to estimate the systematic error in the processof maneuvering target adaptive tracking, a new method is proposed.The proposed method is a linear tracking scheme basedon a modified input estimation approach. A special augmentationin the state space model is considered, in which both the systematicerror and the unknown input vector are attached to thestate vector. Then, an augmented state model and a measurementmodel are established in the case of systematic error, andthe corresponding filter formulas are also given. In the proposedscheme, the original state, the acceleration and the systematicerror vector can be estimated simultaneously. This method can notonly solve the maneuvering target adaptive tracking problem in thecase of systematic error, but also give the system error value inreal time. Simulation results show that the proposed tracking algorithmoperates in both the non-maneuvering and the maneuveringmodes, and the original state, the acceleration and the systematicerror vector can be estimated simultaneously. 展开更多
关键词 systematic error estimation maneuvering target adaptive tracking augmented system model modified input estimationapproach.
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A POSTERIORI ERROR ESTIMATION OF THE NEW MIXED ELEMENT SCHEMES FOR SECOND ORDER ELLIPTIC PROBLEM ON ANISOTROPIC MESHES
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作者 王培珍 陈绍春 《Acta Mathematica Scientia》 SCIE CSCD 2014年第5期1510-1518,共9页
This paper presents a posteriori residual error estimator for the new mixed el-ement scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established with... This paper presents a posteriori residual error estimator for the new mixed el-ement scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established without any regularity assumption on the mesh. 展开更多
关键词 error estimator anisotropic meshes new mixed element schemes
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A-Posteriori Error Estimation for the Legendre Spectral Galerkin Method in One-Dimension
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作者 Lijun Yi Benqi Guo 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2010年第1期40-52,共13页
In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis sh... In this paper, a-posteriori error estimators are proposed for the Legendre spectral Galerkin method for two-point boundary value problems. The key idea is to postprocess the Galerkin approximation, and the analysis shows that the postproeess improves the order of convergence. Consequently, we obtain asymptotically exact aposteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis. 展开更多
关键词 Legendre spectral Galerkin method two-point boundary value problem SUPERCONVERGENCE a-posteriori error estimation.
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Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs
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作者 Karan S. Surana A. D. Joy J. N. Reddy 《Applied Mathematics》 2016年第12期1359-1407,共49页
This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential o... This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the integral form is equivalent, one cannot exist without the other, hence can be used interchangeably. Dimensional model problems consisting of diffusion equation, convection-diffusion equation, and Burgers equation described by self adjoint, non-self adjoint, and nonlinear differential operators are considered to present extensive numerical studies using Galerkin method with weak form (GM/WF) and least squares process (LSP) to determine computed convergence rates of various error norms and present comparisons with the theoretical convergence rates. 展开更多
关键词 Finite Element error estimation Convergence Rate A Priori A Posteriori BVP Variationally Consistent Integral Form Variationally Inconsistent Integral Form Differential Operator Classification SELF-ADJOINT NON-SELF-ADJOINT Nonlinear
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A-posteriori error estimation for second order mechanical systems
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作者 Thomas Ruiner Jrg Fehr +1 位作者 Bernard Haasdonk Peter Eberhard 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第3期854-862,共9页
One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the r... One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies de- grees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of me- chanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advan- tage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demon- strated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted. 展开更多
关键词 A-posteriori error estimator. Flexible multibodysystems Model reduction
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Performance and Improvement of MCS Selection with Channel Quality Estimation Errors for HSDPA
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作者 贾民丽 匡镜明 +1 位作者 万蕾 费泽松 《Journal of Beijing Institute of Technology》 EI CAS 2006年第4期462-466,共5页
The throughput performance of modulation and coding schemes (MCS) selection with channel quality estimation errors (CQEE) is analyzed for high-speed downlink packet access (HSDPA). To reduce the loss of throughp... The throughput performance of modulation and coding schemes (MCS) selection with channel quality estimation errors (CQEE) is analyzed for high-speed downlink packet access (HSDPA). To reduce the loss of throughput caused by CQEE, the robust MCS selection method and adaptive MCS switching scheme are proposed. In addition, automatic repeat request (ARQ) scheme is used to improve the block error rate (BLER) performance. Simulation results show that the proposed methods decrease the throughput loss resulted from CQEE efficiently and BLER performance gets better with ARQ scheme. 展开更多
关键词 high-speed downlink packet access (HSDPA) modulation and coding scheme (MCS) channel quality estimation error (CQEE) automatic repeat request (ARQ)
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A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations
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作者 Yiming Wen Luoping Chen Jiajia Dai 《Journal of Applied Mathematics and Physics》 2023年第2期361-376,共16页
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m... In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator. 展开更多
关键词 Two-Grid Mixed Finite Element Methods Posteriori error Estimates Semilinear Elliptic Equations Averaging Technique
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Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials
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作者 Othman Baiz EL-Hassan Benkhira Rachid Fakhar 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期201-219,共19页
In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coul... In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established. 展开更多
关键词 piezoelectric material frictional contact variational Inequality fixed point process finite element method error estimation iteration method
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The Data Generating Model in Toxicity Test and Estimation for the Toxicity Indicators
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作者 刘迎洲 位刚 +1 位作者 卢恩双 袁志发 《Plant Diseases and Pests》 CAS 2010年第4期42-45,共4页
This paper gives the mathematical reason that the probit analysis method of toxicity measurement is reasonable, and proposes a new approach to compute the interval estimation of median lethal dose and 95% lethal dose.... This paper gives the mathematical reason that the probit analysis method of toxicity measurement is reasonable, and proposes a new approach to compute the interval estimation of median lethal dose and 95% lethal dose. Based on the dose-response function of pesticides, this study firstly establishes a model of the data generating progress in toxicity test and proves that when the linear models of the logarithm of probability value and dose have been estimated, the weighted linear regression should be used, it is the reason why there is the heteroscedasticity of random disturbance term in the regression model, and the weight is right the reciprocal of the variance for random disturbance term. Secondly, based on the numerical simulation method, this paper gives a new approach for the interval estimation of median lethal dose and 95% lethal dose. 展开更多
关键词 Toxicity measurement Probit analysis BOOTSTRAP estimation error Interval estimation
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