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FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div)ELEMENTS

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Journal of Computational Mathematics 2008年第3期26卷 410-436页

作者： Junping Wang Xiaoshen Wang xiu ye Division of Mathematical Sciences National Science Foundation Arlington VA 22230 USA Department of Mathematics University of Arkansas at Little Rock Little Rock AK 72204 USA

We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H（div） conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H（div） finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.

关键词： Finite element methods Navier-Stokes equations CFD

Four-Order Superconvergent Weak Galerkin Methods for the Biharmonic Equation on Triangular Meshes

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Communications on Applied Mathematics and Computation 2023年第4期5卷 1323-1338页

作者： xiu ye Shangyou Zhang Department of Mathematics University of Arkansas at Little RockLittle RockAR72204USA Department of Mathematical Sciences University of DelawareNewarkDE19716USA

A stabilizer-free weak Galerkin(SFWG)finite element method was introduced and analyzed in ye and Zhang(SIAM ***.58:2572–2588,2020)for the biharmonic equation,which has an ultra simple finite element *** work is a continuation of our investigation of the SFWG method for the biharmonic *** new SFWG method is highly accurate with a convergence rate of four orders higher than the optimal order of convergence in both the energy norm and the L^(2)norm on triangular *** new method also keeps the formulation that is symmetric,positive definite,and ***-order superconvergence error estimates are proved for the corresponding SFWG finite element solutions in a discrete H^(2)*** of four orders in the L^(2)norm is also derived for k≥3,where k is the degree of the approximation *** postprocessing is proved to lift a P_(k)SFWG solution to a P_(k+4)solution elementwise which converges at the optimal *** examples are tested to verify the theor ies.

关键词： Finite element Weak Hessian Weak Galerkin(WG) Biharmonic equation Triangular mesh

An adaptive fuzzy filter for coding artifacts removal in video and image

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第6期8卷 841-848页

作者： WU Jing ye xiu-qing GU Wei-kang Department of Information and Communication Engineering Zhejiang University Hangzhou 310027 China

This paper proposes a new adaptive post-filtering algorithm to remove coding artifacts in block-based video coder. The proposed method concentrates on blocking and ringing artifacts removal. For de-blocking, the blocking strength is identified to determine the filtering range, and the maximum quantization parameter of the image is used to adapt the 1D fuzzy filter. For de-ringing, besides the edge detection, a complementary ringing detection method is proposed to locate the neglected ringing blocks, and the gradient threshold is adopted to adjust the parameter of 2D fuzzy filter. Experiments are performed on the MPEG-4 sequences. Compared with other methods, the proposed one achieves better detail preservation and artifacts removal performance with lower computational cost.

关键词： Adaptive fuzzy filter Blocking artifacts Ringing artifacts De-blocking De-ringing

A Mixed Finite-Element Method on Polytopal Mesh

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Communications on Applied Mathematics and Computation 2022年第4期4卷 1374-1385页

作者： Yanping Lin xiu ye Shangyou Zhang Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomHong KongChina Department of Mathematics University of Arkansas at Little RockLittle RockAR 72204USA Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

In this paper,we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic *** establish optimal order error estimates for velocity and super convergence for *** exper... 详细信息

关键词： Mixed finite-element methods Second-order elliptic problem Polytopal mesh

A Modified Weak Galerkin Finite Element Method for the Biharmonic Equation on Polytopal Meshes

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Communications on Applied Mathematics and Computation 2021年第1期3卷 91-105页

作者： Ming Cui xiu ye Shangyou Zhang College of Applied Science Beijing University of TechnologyBeijingChina Department of Mathematics University of Arkansas at Little RockLittle RockAR 72204USA Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

A modified weak Galerkin(MWG)finite element method is developed for solving the biharmonic *** method uses the same finite element space as that of the discontinuous Galerkin method,the space of discontinuous polynomials on polytopal *** its formulation is simple,symmetric,positive definite,and parameter independent,without any of six inter-element face-integral terms in the formulation of the discontinuous Galerkin *** order error estimates in a discrete H2 norm are established for the corresponding finite element *** estimates in the L^(2)norm are also derived with a sub-optimal order of convergence for the lowest-order element and an optimal order of convergence for all high-order of *** numerical results are presented to confirm the theory of convergence.

关键词： Finite element methods Weak Laplacian Biharmonic equations Polytopal meshes

Polarization of ∧'s Produced in S+Pb Collisions at 200 GeV/c per Nucleon

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Chinese Physics Letters 1996年第5期13卷 351-354页

作者： ye Yun-xiu SU Shu-fang JI Gang Department of Modern Physics University of Science arid Technology of ChinaHefei 230027 Department of Special Class for Gifted Young University of Science arid Technology of ChinaHefei 230027

The ∧^(0) polarization is analyzed with the experinental data in S+Pb collisions at energy 200GeV per nucleon,which were produced at SPS of *** *** rxalue and thecorrelation betrween the transverse polarization and transverse momentum were obtained in Feyn-man parameter x_(F)>0,r_(F)<0 and all *** results show that the non-polarization of lamb-da appears in the vegion of larger transterse momenta,say,at 1-2 GeV/c in P_(T).The originsof polarization reduction are discussed.

关键词： GeV/c transverse Polarization

Implementing VLPR systems based on TMS320DM642

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第12期8卷 2005-2016页

作者： ZHU Le-qing ZHANG San-yuan ye xiu-zi School of Computer Science and Technology Zhejiang University Hangzhou 310027 China

This paper gives a practical schema for using DSP boards to construct Vehicle License Plate Recognition (VLPR) modules that could be embedded in any Intelligent Transportation System (ITS). Using DSP can avoid the heavy investment in dedicated VLPR system and improve the computational power compared to PC software environment. Low cost, high computational power, and high flexibility of DSP provide the License Plate Recognition System (LPRS) an excellent cost-effective solution to execute the major part of the recognition tasks. This paper describes a successful implementation of VLPR system based on Texas Instruments (TI)'s TMS320DM642. The DSP board acquires video (which could be output to a monitor for surveillance) from a camera, captures images from the video, locates and recognizes the license plates in images, and then sends the recognized results and related images after compression to a host PC through the network. Finally, the overall software is optimized according to the features of DM642 chip. Experiments showed that the DSP VLPR system performs well on the local license plates, and that the processing speed and accuracy can meet the requirement of practical applications.

关键词： License Plate Recognition (LPR) Embedded system Image processing DSP DM642

A Discontinuous Galerkin Finite Element Method without Interior Penalty Terms

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 299-314页

作者： Fuzheng Gao xiu ye Shangyou Zhang School of Mathematics Shandong UniversityJinanShandong 250100China Department of Mathematics University of Arkansasat Little RockLittle RockAR 72204USA Department of Mathematical Sciences University of DelawareNewarkDE 19716USA

A conforming discontinuous Galerkinﬁnite element method was introduced by ye and Zhang,on simplicial meshes and on polytopal meshes,which has theﬂexibility of using discontinuous approximation and an ultra simple *** main goal of this paper is to improve the above discontinuous Galerkinﬁnite element method so that it can handle nonhomogeneous Dirichlet boundary conditions *** addition,the method has been generalized in terms of approximation of the weak *** estimates of optimal order are established for the correspond-ing discontinuousﬁnite element approximation in both a discrete H1 norm and the L2 *** results are presented to conﬁrm the theory.

关键词： Nonhomogeneous Dirichlet boundary conditions weak gradient discontinuous Galerkin stabilizer penalty free finite element methods polytopal mesh

Equilibrium dividend strategies in the dual model with a random time horizon

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Applied Mathematics(A Journal of Chinese Universities) 2023年第4期38卷 510-522页

作者： ZHAO Yong-xia ye Chuan-xiu CHENG Gong-pin School of Statistics and Data Science Qufu Normal UniversityQufu 273165China School of Mathematical Sciences Qufu Normal UniversityQufu 273165China School of Economics Nanjing University of Finance and EconomicsNanjing 210046China

This paper investigates the dividend problem with non-exponential discounting in a dual *** assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random *** the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification *** the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value ***,numerical examples are shown to illustrate our results.

关键词： equilibrium dividend strategies non-exponential discounting time inconsistence dual model equilibrium HJB-equation