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Volume 12, Issue 2
Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson-Nernst-Planck System

Jie Ding, Cheng Wang & Shenggao Zhou

DOI: 10.4208/nmtma.OA-2018-0058

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 607-626.

Published online: 2018-12

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  • Abstract

In this work, we propose and analyze a second-order accurate numerical scheme, both in time and space, for the multi-dimensional Poisson-Nernst-Planck system. Linearized stability analysis is developed, so that the second order accuracy is theoretically justified for the numerical scheme, in both temporal and spatial discretization. In particularly, the discrete $W^{1,4}$ estimate for the electric potential field, which plays a crucial role in the proof, are rigorously established. In addition, various numerical tests have confirmed the anticipated numerical accuracy, and further demonstrated the effectiveness and robustness of the numerical scheme in solving problems of practical interest.

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@Article{NMTMA-12-607, author = {Jie Ding, Cheng Wang and Shenggao Zhou}, title = {Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson-Nernst-Planck System}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {607--626}, abstract = {

In this work, we propose and analyze a second-order accurate numerical scheme, both in time and space, for the multi-dimensional Poisson-Nernst-Planck system. Linearized stability analysis is developed, so that the second order accuracy is theoretically justified for the numerical scheme, in both temporal and spatial discretization. In particularly, the discrete $W^{1,4}$ estimate for the electric potential field, which plays a crucial role in the proof, are rigorously established. In addition, various numerical tests have confirmed the anticipated numerical accuracy, and further demonstrated the effectiveness and robustness of the numerical scheme in solving problems of practical interest.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0058}, url = {http://global-sci.org/intro/article_detail/nmtma/12911.html} }
TY - JOUR T1 - Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson-Nernst-Planck System AU - Jie Ding, Cheng Wang & Shenggao Zhou JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 607 EP - 626 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0058 UR - https://global-sci.org/intro/article_detail/nmtma/12911.html KW - AB -

In this work, we propose and analyze a second-order accurate numerical scheme, both in time and space, for the multi-dimensional Poisson-Nernst-Planck system. Linearized stability analysis is developed, so that the second order accuracy is theoretically justified for the numerical scheme, in both temporal and spatial discretization. In particularly, the discrete $W^{1,4}$ estimate for the electric potential field, which plays a crucial role in the proof, are rigorously established. In addition, various numerical tests have confirmed the anticipated numerical accuracy, and further demonstrated the effectiveness and robustness of the numerical scheme in solving problems of practical interest.

Jie Ding, Cheng Wang and Shenggao Zhou. (2018). Optimal Rate Convergence Analysis of a Second Order Numerical Scheme for the Poisson-Nernst-Planck System. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 607-626. doi:10.4208/nmtma.OA-2018-0058
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