2002年, 第20卷, 第1期　刊出日期：2002-01-15

  

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  A HIGHLY ACCURATE NUMERICAL METHOD FOR FLOW PROBLEMS WITH INTERACTIONS OF DISCONTINUITIES

  Xiao Nan WU(1),You Lan ZHU(2)

  Journal of Computational Mathematics. 2002, 20(1): 1-014.

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  A type of shock fitting method is used to solve some two and three dimensional flow problems with interactions of various discontinuities. The numerical results show that high accuracy is achieved for the flow field, especially at the discontinuities. Comparisons with the Lax-Friedrichs scheme and the ENO scheme confirm the accuracy of the method.
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  LINEAR FINITE ELEMENT APPROXIMATIONS FOR THE TIMOSHENKO BEAM AND THE SHALLOW ARCH PROBLEMS

  Xiao Liang CHENG(1),Wei Min XUE(2)

  Journal of Computational Mathematics. 2002, 20(1): 15-022.

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  In this paper we discuss the linear finite element approximations for the Timoshenko beam and the shallow arch problems with shear dampening and reduced integration. We derive directly the optimal order error estimates uniformly with the small thickness parameter, without relying on the theory of saddle point problems.
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  MODIFIED PARALLEL ROSENBROCK METHODS FOR STIFF DIFFERENTIAL EQUATIONS

  Xue Nian CAO(1),Shou Fu LI(1),De Gui Liu(2)

  Journal of Computational Mathematics. 2002, 20(1): 23-034.

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  To raise the efficiency of Rosenbrock methods Chen Lirong and Liu Degui have con- structed the parallel Rosenbrock methods in 1995, which are written as PRMs for short. In this paper we present a class of modified parallel Rosenbrock methods which possesses more free parameters to improve further the various appropriately, we search out the practically optimal 2-stage 3rd-order and 3-stage 4th-order MPROWs, which are all A-stable and have small error constants. Theoretical analysis and numerical experiments showthat for solving stiff problems the MPROWs searched out in the present paper are much more efficient than the existing parallel and sequential methods of the same type and same order mentioned above.
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  ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

  Lan Chieh HUANG

  Journal of Computational Mathematics. 2002, 20(1): 35-056.

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  The unsteady incompressible Navier-Stokes equations are discretized in space and stud- ied on the fixed mesh as a system of differential algebraic equations. With discrete projec- tion defined, the local errors of Crank Nicholson schemes with three projection methods are derived in a straightforward manner. Then the approximate factorization of relevant matrices are used to study the time accuracy with more detail,especially at points adjacent to the boundary. The effects of numerical boundary conditions for the auxiliary velocith and the discrete pressure Poisson equation on the time accuracy are also investigated.Results of numerical experiments with an analytic example confirm the conclusions of our analysis.
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  A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE ADVECTION-DIFFUSION EQUATIONS

  Huo Yuan DUAN

  Journal of Computational Mathematics. 2002, 20(1): 57-064.

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  This paper is devoted to the development of a new stabilized finite element method for solving the advection-diffusion equations having the form $-\kappa\Delta u+\underline{a}\bullet\underline{\nabla}u+\sigma u=f$ with a zero Dirichlet boundary condition. We show that this methodology is coercive and has a uniformly optimal convergence result for all mesh-Peclet number.
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  CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

  Ben Yu GUO(1),Song Nian He(2),He Ping MA(3)

  Journal of Computational Mathematics. 2002, 20(1): 65-078.

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  A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensional unsteady Navier-Stokes equation. The generalized stability and convergence are proved. The numerical results show the advantages of this method.
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  ERROR ANALYSIS AND GLOBAL SUPERCONVERGENCES FOR THE SIGNORINI PROBLEM WITH LAGRANGE MULTIPLIER METHODS

  Ping LUO(1),Guo Ping LIANG(2)

  Journal of Computational Mathematics. 2002, 20(1): 79-088.

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  In this paper, the finite element approximation of the Signorini problem is studied by using Lagrange multiplier methods with piecewise constant elements. Optimal error bounds are obtained and iterative algorithm and its convergence are given. Furthermore, global superconvergences are proved.
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  A NOTE ON THE CONSTRUCTION OF SYMPLECTIC SCHEMES FOR SPLITABLE HAMILTONIAN H = H~((1)) + H~((2)) + H~((3))

  Yi Fa TANG

  Journal of Computational Mathematics. 2002, 20(1): 89-096.

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  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 parameters for splitable hamiltonian $H=H^{(1)}+H^{(2)}+H^{(3)}$.
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  RELAXED ASYNCHRONOUS ITERATIONS FOR THE LINEAR COMPLEMENTARITY PROBLEM

  Zhong Zhi BAI(1),Yu Guang HUANG(2)

  Journal of Computational Mathematics. 2002, 20(1): 97-112.

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  We present a class of relaxed asynchronous parallel multisplitting iterative methods for solving the linear complementarily problem on multiprocessor systems, and set up their convergence theories when the system matrix of the linear complementar complementarity problem is an H-matrix with positive diagonal elements.