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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

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.

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

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.

FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 225-238页

作者： Jian Li (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.

关键词： Navier-Stokes equations Fourier-Legendre pseudospectral method error estimation

ON THE CENTRAL RELAXING SCHEMES I:SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 2000年第3期18卷 313-324页

作者： Hua-zhong Tang (LSEC, Institute of Computational mathematics and Scientific /Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality

A TRUST REGION METHOD FOR SOLVING DISTRIBUTED PARAMETER IDENTIFICATION PROBLEMS

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Journal of Computational mathematics 2003年第6期21卷 759-772页

作者： Yan-fei Wang Ya-xiang Yuan(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

This paper is concerned with the ill-posed problems of identifying a parameter in an elliptic equation which appears in many applications in science and industry. Its solution is obtained by applying trust region method to a nonlinear least squares error problem. Trust region method has long been a popular method for well-posed problems. This paper indicates that it is also suitable for ill-posed problems. Numerical experiment is given to compare the trust region method with the Tikhonov regularization method. It seems that the trust region method is more promising.

关键词： Parameter identification Ill-posed problems Trust region.

THE L^2-NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2ND ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGULARITY

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Journal of Computational mathematics 2000年第3期18卷 277-282页

作者： Lie-heng Wang (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.

关键词： L-2-norm error estimate nonconforming f.e.m. lowest regularity