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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (2): 179-192.doi: 10.3969/j.issn.1005-3085.2018.02.005

• • 上一篇    下一篇

对流扩散方程的特征线EFG算法

童小红,   王   兴,   苏李君,   胡   钢,   秦新强   

  1. 西安理工大学应用数学系，西安  710048
  • 收稿日期:2016-01-28 接受日期:2016-07-12 出版日期:2018-04-15 发布日期:2018-06-15
  • 基金资助:
    国家自然科学基金(51409212; 51305344)；陕西省教育厅基金(16JK1558).

Characteristic Element Free Galerkin Method for Convection-dominated Diffusion Equations

TONG Xiao-hong,  WANG Xing,  SU Li-jun,  HU Gang,  QIN Xin-qiang   

  1. Department of Applied Mathematics, Xi'an University of Technology, Xi'an 710048
  • Received:2016-01-28 Accepted:2016-07-12 Online:2018-04-15 Published:2018-06-15
  • Supported by:
    The National Natural Science Foundation of China (51409212; 51305344); the Foundation of Shaanxi Province Department of Education (16JK1558).

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摘要： 为了消除对流扩散方程因对流占优引起的数值震荡，本文首先将其转化为特征形式，并利用移动最小二乘基函数，构建了特征线无单元Galerkin方法．再对新建方法进行收敛性分析，分别给出关于支持域半径和时间步长的两种误差估计．最后，分别针对一维和二维算例进行了数值计算，并与有限元法进行了比较．数值结果表明，本文算法收敛性好，可以消除数值震荡，且通过选取合适的罚因子和支持域的无量纲尺寸，计算精度比有限元法更高，是求解对流占优扩散方程的一种有效程数值计算方法．

关键词: 对流扩散方程, 无单元Galerkin方法, 移动最小二乘, 误差分析

Abstract: In order to eliminate the numerical oscillation caused by convection dominant of convection diffusion equation, the equation is transformed into its characteristics form firstly, and then the element free Galerkin method is proposed by using the moving least square basis functions. The convergence analysis of our method is analyzed, and two kinds of error analysis about the radius of the influence domain and time step are derived, respectively. The numerical examples are presented to discuss the comparison the new method with the finite element method as well. The numerical results show that the new method can be used to eliminate the numerical oscillation with a good convergence. Moreover, the accuracy of the new method is better than the finite element method by choosing the optimal penalty factor and dimensionless size. The new method is an effective numerical method for solving the convection-dominant diffusion equations.

Key words: convection diffusion equations, element free Galerkin method, moving least square basis function, error analysis

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