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A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method

ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 35-56页

作者： Lan Chieh Huang (ICMSEC, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the fully implicit Crank Nicholson (CN) schemes and three projection methods for approximate preservation of component-consistency under projection. Transformation from incompressible Navier-Stokes equations to differential algebraic equations CN schemes; Local errors of CN projection methods; Numerical boundary conditions.

关键词： differential algebraic equations discrete projection numerical boundary conditions

CONVERGENCE OF VORTEX METHODS FOR 3-D EULER EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of system science, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china School of Mathematical sciences, Peking University, beijing 100871, china) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

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Journal of Computational mathematics 2003年第5期21卷 613-624页

作者： Pu-yan Nie(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.

关键词： Composite-step like approaches Filter methods Equality constraints Sequen- tial quadratic programming(SQP) algorithms Normal component Tangential component Convergence.

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

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Journal of Computational mathematics 2003年第6期21卷 733-746页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3/4) and O(h3/2) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

关键词： Dual Mixed Method Unilateral Problem.

Transformations and non-degenerate maps

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science china mathematics 2005年第Z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei Institute of mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Graduate School Chinese Academy of Sciences Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

SYMPLECTIC COMPUTATION OF HAMILTONIAN systemS (I)

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Journal of Computational mathematics 2002年第3期20卷 267-276页

作者： Yi-fa Tang(LSEC,ICMSEC,academy of mathematics and system sciences, chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

Presents information on a study which discussed a symplectic computation of hamiltonian systems. Terms of formal energy of mid-point rule; Analysis of the mathematical pendulum to test the convergence of the formal en... 详细信息

关键词： mid-point rule formal energy

A NOTE ON THE CONSTRUCTION OF SYMPLECTIC SCHEMES FOR SPLITABLE HAMILTONIAN H = H^((1)) + H^((2)) + H^((3))

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Journal of Computational mathematics 2002年第1期20卷 89-96页

作者： Yi-fa Tang (LSEC ICMSEC academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In this note, we will give a proof for the uniqueness of 4th-order time-reversible sym- plectic difference schemes of 13th-fold compositions of phase flows φtH(1) , φtH(2) , φtH(3) with different temporal parameter... 详细信息

关键词： Time-Reversible symplectic scheme Splitable hamiltonian.

GAUSS-SEIDEL-TYPE MULTIGRID METHODS

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Journal of Computational mathematics 2003年第4期21卷 421-434页

作者： Zhao-hui Huang Qian-shun Chang (academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) academy of mathematics and system sciences Chinese Academy of Sciences 北京 100080

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity.

关键词： Multigrid methods Gauss-Seidel solution Interpolation formula Convergence.