东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2008, Vol. 29 ›› Issue (8): 1204-1208.DOI: -

• 论著 • 上一篇    下一篇

矩形网格抛物型问题的质量集中有限元方法

李铮;张铁;李长军;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2008-08-15 发布日期:2013-06-22
  • 通讯作者: Li, Z.
  • 作者简介:-
  • 基金资助:
    国家自然科学基金资助项目(10771031)

Lumped mass finite element method for parabolic problem on rectangular mesh

Li, Zheng (1); Zhang, Tie (1); Li, Chang-Jun (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2008-08-15 Published:2013-06-22
  • Contact: Li, Z.
  • About author:-
  • Supported by:
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摘要： 就一类典型的抛物型问题——热传导方程,研究矩形网格上质量集中有限元方法的有关性质.首先给出了矩形单元上双线性有限元基函数的积分公式,在此基础上讨论质量集中有限元方法的误差估计.研究表明,矩形网格上的质量集中有限元方法具有与普通的有限元方法同等的逼近精度,但却具有更少的计算量,并且在一定条件下可以保持极值性质.最后给出了在矩形网格上质量集中有限元方法保持极值性质的剖分条件.

关键词: 质量集中有限元方法, 抛物型问题, 有限元方法, 极值性质, 热传导方程

Abstract: The property of the lumped mass finite element method (LMFEM) on rectangular mesh is investigated to solve a typical parabolic problem, i.e., the heat transfer equation. The integral formula of the bi-linear finite element basis function on the rectangular mesh is given to discuss the error estimation for LMFEM. It is found that LMFEM has the equivalent approximate accuracy to the standard finite element method on the rectangular mesh, while the former has less computational cost and can retain the maximum principle under certain conditions. Moreover, the partitioning conditions for retaining the maximum principle on rectangular mesh are given.

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