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稳态Poisson-Nernst-Planck方程的残量型后验误差估计

房明娟, 阳莺, 唐鸣   

  1. 桂林电子科技大学数学与计算科学学院, 桂林 541004
  • 收稿日期:2019-03-12 发布日期:2021-02-04
  • 通讯作者: 阳莺, Email: yangying@lsec.cc.ac.cn
  • 基金资助:
    国家自然科学基金(11561016,11701119,11771105);广西自然科学基金项目(2017GXNSFFA 198012,2017GXNSFFA198056,2020GXNSFAA159098);广西高校数据分析与计算重点实验室开放基金资助项目;湘潭大学科学工程计算与数值仿真湖南省重点实验室开放课题基金资助.

房明娟, 阳莺, 唐鸣. 稳态Poisson-Nernst-Planck方程的残量型后验误差估计[J]. 计算数学, 2021, 43(1): 17-32.

Fang Mingjuan Yang Ying Tang Ming. RESIDUAL-TYPE A POSTERIORI ERROR ESTIMATES FOR STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS[J]. Mathematica Numerica Sinica, 2021, 43(1): 17-32.

RESIDUAL-TYPE A POSTERIORI ERROR ESTIMATES FOR STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS

Fang Mingjuan Yang Ying Tang Ming   

  1. School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
  • Received:2019-03-12 Published:2021-02-04
针对稳态的Poisson-Nernst-Planck方程研究了一种残量型的后验误差估计子, 对方程的两个解-浓度和电势, 都分别给出了上界和下界估计. 数值实验表明, 基于这种后验误差估计子构造的自适应有限元算法对于稳态的Poisson-Nernst-Planck方程是有效的.
A residual posteriori error estimator is studied for the Steady-state Poisson-NernstPlanck equations. The upper and lower bounds of the concentration and potential solutions of the equations are estimated respectively. The numerical experiments show that the adaptive finite element algorithm based on the a posteriori error estimator is effective for the steadystate Poisson-Nernst-Planck equations.

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