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《Numerical Mathematies A Journal of Chinese Universities》 1998-01
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ON A CLASS OF GENERALIZED DIFFERENCE METHODS WITH BB DUAL SUBDIVISION

Li Yonghai Li Ronghua(Jilin University)  
In this paper, the authors discuss a class of generalized difference methods for the boundary value problems of second order elliptic equationLet Th be the triangulation subdivisions of domain Ω and the tried spaces Uh H01(Ω) which consist of the piece-wise linear function on Th, Let Th* be the dual subdivisions in association with Th , where any element is constructed by connecting bar-rycenters of two triangular elements in Th with common edge in turn and simply called it the BB dual element. Then the test spaces Vh L2(Ω) consist of the step function on TVh*. Denoting by a(u,v) the bilinear form corresponding to the problem ( Ω ) , then the generalized difference approximation uh is defined by the following e-quationa(uh,vh) = (f,vh),   vh∈Vh.A similar method has been applicated in the computational fluid dynamics (cf. [3] [4]) , but there were no any theoretical result to our knowledge. The purpose of the paper is to establish the error estimate with an optimal order under some restriction on the subdivisiion. The effect of the method is evident by the numerical experiment also.
【CateGory Index】: O241.8
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【References】
Chinese Journal Full-text Database 3 Hits
1 Liu Xiaohua Xie Xiangjun (Dept. of Comput. Sci., Southwest Petroleum Institute, Nanchong 637001);THE L~2-NORM ERROR ESTIMATE FOR GENERALIZED DIFFERENCE SCHEME BASED ON BB DUAL SUBDIVISIONS[J];Numerical Mathematics A Journal of Chinese Universities;2003-01
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3 Li Yonghai Cheng Zhiwei (Department of Mathematics, Jilin University, Changchun 130012, China) Sun Fengzhi (Deparment of Mathematics, Daqing Normal College, Daqing 163712, China);THE FINITE VOLUME ELEMENT METHOD FOR PARABOLIC EQUATION ON BB DUAL SUBDIVISIONS[J];Mathematica Numerica Sinica;2005-04
【Citations】
Chinese Journal Full-text Database 1 Hits
1 Li Yunghua Zhu Piqi (Jilin University);GENERALIZED DIFFERENCE METHODS FOR 2ND ORDER ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS[J];Numerical Mathematics A Journal of Chinese Universities;1982-02
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 MA Rui-jie~(1),LI Xin~(2)(1.College of Mathematics,Jilin University,Changchun130026,China;2.College of Construction Engineering,Jilin University,Changchun130026,China);The Finite Element Volume Method and Application of Mathematic Model of Karst Groundwater Flow[J];Journal of Jiling University (Earth Science Edition);2005-06
2 TANG Li-min, QI Zhao-hui, DING Ke-wei, TIAN Zhong-xu, HE Dong-sheng ( Dept. of Eng. Mech., Dalian Univ. of Technol., Dalian 116024, China );Establishment and applications of weak form generalized basic equations in elasticity[J];Journal of Dalian University of Technology;2001-01
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4 Liang Dong(Shandong University);THE NUMERICAL METHOD OF THE DISCRECTE OPERATOR FOR THREE-DIMENSIONAL NONLINEAR PARABOLIC EQUATIONS[J];Chinese Journal of Engineering Mathematics;1988-01
5 FENG Lianhai(Basic Courses Division, Zhongzhou University, Zhengzhou 450005);A Finite Volume Element Scheme for Solving Second Order Elliptic Partial Differential Equations[J];Chinese Journal of Engineering Mathematics;2002-04
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9 Ni Ping (North-East Normal University);GENERALIZED METHODS FOR SOLVING THE BEAM EQUILIBRIUM EQUATIONS[J];Numerical Mathematics A Journal of Chinese Universities;1984-04
10 Li Qian(Shandong University);THE GENERALIZED GALERKIN METHOD FOR THE ELLIPTICAL TYPE EQUATIONS WITH THE THIRD BOUNDARY CONDITION[J];Numerical Mathematics A Journal of Chinese Universities;1986-01
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1 WU Zheng-peng ,LI Lin ,YU De-hao (Department of Applied Mathematics,Beijing broadcasting Institute,Beijing 100024 P.R.China; Academy of Mathematics & System Sciences, CAS,Beijing 100080 P.R.China);The Overlapping Demoposition Method For 2-D Exterior Elliptic Problem Based on the Natural Boundary Reduction[J];Journal of Beijing Broadcasting Institute;2004-01
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【Secondary References】
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1 CHENG Zhi-wei, LI Yong-hai (College of Mathematics, Jilin University, Changchun 130012, China);Finite volume element method of parabolic equation based on BB dual subdivisions[J];Acta Scientiarium Naturalium Universitatis Jilinensis;2004-02
2 SUN Feng-zhi~(1,2), LI Yong-hai~1(1. Department of Information and Computation, College of Mathematics, Jilin University, Changchun 130012, China;2. Department of Mathematics, Daqing Normal College, Daqing 163712, China);Finite Volume Element Method Based on Circumcenter Dual Subdivisions[J];Journal of Jilin University (Science Edition);2005-01
3 Li Yonghai Cheng Zhiwei (Department of Mathematics, Jilin University, Changchun 130012, China) Sun Fengzhi (Deparment of Mathematics, Daqing Normal College, Daqing 163712, China);THE FINITE VOLUME ELEMENT METHOD FOR PARABOLIC EQUATION ON BB DUAL SUBDIVISIONS[J];Mathematica Numerica Sinica;2005-04
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