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粘弹性方程全离散化有限体积元格式及数值模拟

李宏1, 孙萍2, 尚月强2, 罗振东2   

  1. 1. 内蒙古大学数学科学学院, 呼和浩特 010021;
    2. 贵州师范大学数学与计算机科学学院, 贵阳 550001
  • 收稿日期:2011-11-30 出版日期:2012-11-15 发布日期:2012-11-12
  • 基金资助:

    国家自然科学基金(批准号: 11061009、11061021和11271127);河北省自然科学基金(批准号: A2010001663);内蒙古自然科学基金(批准号:2012MS0106);贵州省科技计划课题(批准号:QKJ[2011]2367)和内蒙古自治区高等学校研究项目(批准号: NJ10006)

李宏, 孙萍, 尚月强, 罗振东. 粘弹性方程全离散化有限体积元格式及数值模拟[J]. 计算数学, 2012, 34(4): 413-424.

Li Hong, Sun Ping, Shang Yueqiang, Luo Zhendong. A FULLY DISCRETE FINITE VOLUME ELEMENT FORMULATION AND NUMERICAL SIMULATIONS FOR VISCOELASTIC EQUATIONS[J]. Mathematica Numerica Sinica, 2012, 34(4): 413-424.

A FULLY DISCRETE FINITE VOLUME ELEMENT FORMULATION AND NUMERICAL SIMULATIONS FOR VISCOELASTIC EQUATIONS

Li Hong1, Sun Ping2, Shang Yueqiang2, Luo Zhendong2   

  1. 1. School of Mathematical Sciences, Inner Mongolia University, Huhhot 010021, China;
    2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China
  • Received:2011-11-30 Online:2012-11-15 Published:2012-11-12
本文利用有限体积元方法研究二维粘弹性方程, 给出一种时间二阶精度的全离散化有限体积元格式, 并给出这种全离散化有限体积元解的误差估计, 最后用数值例子验证数值结果与理论结果是相吻合的. 通过与有限元方法和有限差分方法相比较, 进一步说明了全离散化有限体积元格式是求解二维粘弹性方程数值解的最有效方法之一.
In this paper, two-dimensional (2D) viscoelastic equations are studied with a finite volume element (FVE) method, a fully discrete finite volume element formulation with second order time accuracy is established, and the error estimates of the discrete FVE solutions are provided. A numerical example is used to illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it has shown that the fully discrete FVE formulation is one of the most efficient for finding numerical solutions of 2D viscoelastic equations by comparing with the numerical results of a fully discrete finite element formulation and a finite difference scheme.

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