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Volume 12, Issue 6
Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations

Ruigang Shen, Shi Shu, Ying Yang & Mingjuan Fang

DOI: 10.4208/aamm.OA-2019-0046

Adv. Appl. Math. Mech., 12 (2020), pp. 1353-1383.

Published online: 2020-09

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  • Abstract

In this article, we derive the a posteriori error estimators for a class of steady-state Poisson-Nernst-Planck equations. Using the gradient recovery operator, the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations. It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.

  • Keywords

Poisson-Nernst-Planck equations, gradient recovery, a posteriori error estimate.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1353, author = {Shen , RuigangShu , ShiYang , Ying and Fang , Mingjuan}, title = {Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {1353--1383}, abstract = {

In this article, we derive the a posteriori error estimators for a class of steady-state Poisson-Nernst-Planck equations. Using the gradient recovery operator, the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations. It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0046}, url = {http://global-sci.org/intro/article_detail/aamm/18292.html} }
TY - JOUR T1 - Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations AU - Shen , Ruigang AU - Shu , Shi AU - Yang , Ying AU - Fang , Mingjuan JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1353 EP - 1383 PY - 2020 DA - 2020/09 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0046 UR - https://global-sci.org/intro/article_detail/aamm/18292.html KW - Poisson-Nernst-Planck equations, gradient recovery, a posteriori error estimate. AB -

In this article, we derive the a posteriori error estimators for a class of steady-state Poisson-Nernst-Planck equations. Using the gradient recovery operator, the upper and lower bounds of the a posteriori error estimators are established both for the electrostatic potential and concentrations. It is shown by theory and numerical experiments that the error estimators are reliable and the associated adaptive computation is efficient for the steady-state PNP systems.

Shen , RuigangShu , ShiYang , Ying and Fang , Mingjuan. (2020). Gradient Recovery-Type a Posteriori Error Estimates for Steady-State Poisson-Nernst-Planck Equations. Advances in Applied Mathematics and Mechanics. 12 (6). 1353-1383. doi:10.4208/aamm.OA-2019-0046
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