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反应扩散方程的连续时空有限元方法

李宏, 杜春瑶, 赵智慧   

  1. 内蒙古大学数学科学学院, 呼和浩特 010021
  • 收稿日期:2016-05-09 出版日期:2017-05-15 发布日期:2017-07-18
  • 基金资助:

    国家自然科学基金(11361035,11301258,11501311),内蒙古自然科学基金(2014BS0101),内蒙古高等学校科学研究项目(NJZY14013).

李宏, 杜春瑶, 赵智慧. 反应扩散方程的连续时空有限元方法[J]. 计算数学, 2017, 39(2): 167-178.

Li Hong, Du Chunyao, Zhao Zhihui. CONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR REACTION DIFFUSION EQUATION[J]. Mathematica Numerica Sinica, 2017, 39(2): 167-178.

CONTINUOUS SPACE-TIME FINITE ELEMENT METHOD FOR REACTION DIFFUSION EQUATION

Li Hong, Du Chunyao, Zhao Zhihui   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • Received:2016-05-09 Online:2017-05-15 Published:2017-07-18
本文研究了反应扩散方程的连续时空有限元方法.首先建立了其连续时空有限元格式并证明了有限元解的存在唯一性及稳定性.然后通过引入时空投影算子在没有时空网格限制的条件下给出其近似解在节点处的,L2,,H2最优范数估计以及全局,L2L2),L2H2)最优范数估计.最后给出两个数值算例来验证方法的有效性与灵活性并说明结论的正确性.
In this paper,we study the continuous space-time element method for reaction-diffusion equation.Firstly,we establish the continuous space-time finite element scheme and prove the existence,uniqueness,and stability of the finite element solution.And then,we not only give the optimal order estimates in L2,H2 norms in time nodes but also give the optimal order estimates in global L2(L2),L2(H2) norms which do not need any restriction conditions between the space and time mesh size by introducing space-time projection operators.Finally,two numerical examples are provided to validate the effectiveness and feasibility of the method and the correctness of the theoretical analyses.

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