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对流扩散方程迎风有限元的自适应方法

赵志勇,胡健伟,孙琳   

  1. 南开大学数学学院科学计算所与教育部核心数学与组合数学实验室 南开大学、天津大学联合研究院应用数学中心,南开大学数学学院科学计算所与教育部核心数学与组合数学实验室 南开大学、天津大学联合研究院应用数学中心,南开大学数学学院科学计算所与教育部核心数学与组合数学实验室 南开大学、天津大学联合研究院应用数学中心 天津 300071 ,天津 300071 ,天津 300071
  • 出版日期:2005-04-14 发布日期:2005-04-14

赵志勇,胡健伟,孙琳. 对流扩散方程迎风有限元的自适应方法[J]. 计算数学, 2005, 27(4): 337-354.

ADAPTIVE UPWIND FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS

  1. Zhao Zhiyong Hu Jianwei Sun Lin (ISC and LPMC, School of Mathematical Science, Nankai University; CAM, United Academy of Nankai University and Tianjin University, Tianjin 300071, China)
  • Online:2005-04-14 Published:2005-04-14

本文对二维发展型对流扩散方程的迎风有限元格式给出了显式后验误差估计,证明了真实误差被后验误差估计器上下界定;并通过误差估计器建立了相应的自适应算法,数值例子表明了方法的有效性.

The explicit a posterior error estimators of upwind finite element for two dimensional evolution convection-diffusion equations are formulated and the above and below bound of estimator compared with true error are proved. An adaptive method based on these estimators is then proposed and numerical results show the efficiency of our method.

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[1] M. Ainsworth, J.T. Oden, A Posteriori Error Estimation in Finite Element Analysis, John Wiley & Sons, Inc, 2000.
[2] L. Angermann, An a posteriori estimation for the solution of elliptic boundary value problems by means of upwind FEM, IMA Journal of Numerical Analysis, 12(1992), 201-215.
[3] I. Babuska, R. Duran, R. Rodriguez, Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements, SIAM J. Numer. Anal., 29:4 (1992), 947- 964.
[4] P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, 1978.
[5] P. Clement, Approximation by finite element functions using local regularization, RAIRO Anal. Num., 9(1975) 77-84.
[6] M. Picasso, Adaptive finite elements for a linear parabolic problem, Comput. Methods Appl. Mech. Engrg., 167 (1998), 223-237.
[7] H.G. Roos, M. Stynes, L. Tobiska, Numerical methods for Singularly Perturbed Differential Equations, Springer, Berlin, 1996.
[8]田春松,胡健伟,一类三角形网格的局部加密方法及其应用,数值计算与计算机应用,23:2(2002),97- 104.
[9]赵志勇,对流扩散问题的迎风有限元格式及其自适应方法,南开大学博士学位论文,2004年4月.

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