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LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM

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Journal of Computational mathematics 2000年第4期18卷 353-364页

作者： Lie-heng Wang Huo-yuan Duan (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

In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]

关键词： least-squares method mixed finite element approximation saddle-point problem

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

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Journal of Computational mathematics 2001年第6期19卷 651-672页

作者： Zhong-zhi Bai (LSEC ICMSEC, academy of mathematics and systems sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic ... 详细信息

关键词： elliptic boundary value problem system of linear equations symmetric positive definite matrix multilevel iteration parallel method

THE PRIMAL-DUAL POTENTIAL REDUCTION ALGORITHM FOR POSITIVE SEMI-DEFINITE PROGRAMMING

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Journal of Computational mathematics 2003年第3期21卷 339-346页

作者： Si-ming Huang(Institute of Policy and Management, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china) Institute of Policy and Management Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

In this paper we introduce a primal-dual potential reduction algorithm for positive semi-definite programming. Using the symetric preserving scalings for both primal and dual interior matrices, we can construct an algorithm which is very similar to the primal-dual potential reduction algorithm of Huang and Kortanek [6] for linear programming. The complexity of the algorithm is either O(nlog(X0 · S0/ε) or O(nlog(X0· S0/ε) depends on the value of ρ in the primal-dual potential function, where X0 and S0 is the initial interior matrices of the positive semi-definite programming.

关键词： Positive semi-definite programming Potential reduction algorithms Complexity.

Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 19-24页

作者： Da-chuan XuInstitute of Applied mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Institute of Applied mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the ... 详细信息

关键词： Keywords Quasi-Newton method Broyden class non-monotone linesearch global convergence unconstrained optimization

Energy Scattering for the Generalized Davey-Stewartson Equations

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Acta Mathematicae Applicatae Sinica 2003年第2期19卷 333-340页

作者： Cheng-chun Haoacademy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china academy of mathematics and system sciences Chinese Academy of Sciences Beijing China

Abstract Considering the generalized Davey-Stewartson equation $i\mathop u\limits^. - \Delta u + \lambda \left| u \right|^p u + \mu E\left( {\left| u \right|^q } \right)\left| u \right|^{q - 2} u = 0$ where $\lambda > 0,\mu \ge 0,E = F^{ - 1} \left( {\xi _1^2 /\left| \xi \right|^2 } \right)F$ we obtain the existence of scattering operator in ^(A↑^n) := { u ] H1(A↑^n) : |x|u ] L2(A↑^n)}.

关键词： Keywords Generalized Davey-Stewartson equation pseudo conformally invariant conservation law scattering operator

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational mathematics 2000年第6期18卷 561-566页

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

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

Adaptive computation for convection dominated diffusion problems

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science china mathematics 2004年第Z1期47卷 22-31页

作者： CHEN Zhiming & Jl GuanghuaLSEC, Institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china Institute of Computational mathematics, academy of mathematics and system sciences, chinese academy of sciences, beijing 100080, china (email:ghji@***) LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Institute of Computational mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

We derive sharp L∞(L1) a posteriori error estimate for the convection dominated diffusion equations of the formThe derived estimate is insensitive to the diffusion parameter ε→0. The problem is dis-cretized implicitly in time via the method of characteristics and in space via continuous piecewise linear finite elements. Numerical experiments are reported to show the competitive behavior of the proposed adaptive method.

关键词： a posteriori error estimator, characteristics, adaptive.

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ON KORN'S INEQUALITY

Journal of Computational mathematics 2003年第3期21卷 321-324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

This paper is devoted to give a new proof of Korn's inequality in LT - norm (1 < γ < ∞).

关键词： Korn's inequality.

Transcendence of Certain Trigonometric Series

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Acta Mathematica Sinica,English Series 2002年第3期18卷 481-488页

作者： Yao Chen ZHU academy of mathematics and system sciences. The chinese academy of sciences, beijing 100080. P. R. china academy of mathematics and system sciences The Chinese Academy of Sciences Beijing P. R. China

In this paper the transcendence of values of certain trigonometric series with algebraic coefficients and its derivatives at algebraic points is proved under a general condition dependent only on the coefficients. The... 详细信息

关键词： Transcendence Trigonometric series Linear independence Number field