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Volume 14, Issue 2
A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids

Zhiyong Si, Piaopiao Dong & Yunxia Wang

Adv. Appl. Math. Mech., 14 (2022), pp. 386-414.

Published online: 2022-01

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  • Abstract

In this paper, a numerical method for the electroneutral micro-fluids based on the finite element method will be given. In order to deal with the non-linearity of the equation, the modified characteristics method will be used to deal with the temporal derivative term and the convective term. In this way, the non-linear equation can be linearized. Then, we will give the unconditional stability and optimal error estimation. At last, some numerical results are given to show the effectiveness of our method. From the stability analysis we can see that the method is unconditionally stable. The numerical results show that our method is robust.

  • AMS Subject Headings

76M10, 65N12, 65N30, 35K61

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-386, author = {Si , ZhiyongDong , Piaopiao and Wang , Yunxia}, title = {A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {386--414}, abstract = {

In this paper, a numerical method for the electroneutral micro-fluids based on the finite element method will be given. In order to deal with the non-linearity of the equation, the modified characteristics method will be used to deal with the temporal derivative term and the convective term. In this way, the non-linear equation can be linearized. Then, we will give the unconditional stability and optimal error estimation. At last, some numerical results are given to show the effectiveness of our method. From the stability analysis we can see that the method is unconditionally stable. The numerical results show that our method is robust.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0327}, url = {http://global-sci.org/intro/article_detail/aamm/20203.html} }
TY - JOUR T1 - A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids AU - Si , Zhiyong AU - Dong , Piaopiao AU - Wang , Yunxia JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 386 EP - 414 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0327 UR - https://global-sci.org/intro/article_detail/aamm/20203.html KW - Electroneutral micro-fluids, finite element method, modified characteristics method, unconditional stability, optimal error estimation. AB -

In this paper, a numerical method for the electroneutral micro-fluids based on the finite element method will be given. In order to deal with the non-linearity of the equation, the modified characteristics method will be used to deal with the temporal derivative term and the convective term. In this way, the non-linear equation can be linearized. Then, we will give the unconditional stability and optimal error estimation. At last, some numerical results are given to show the effectiveness of our method. From the stability analysis we can see that the method is unconditionally stable. The numerical results show that our method is robust.

Zhiyong Si, Piaopiao Dong & Yunxia Wang. (2022). A Modified Characteristics Finite Element Method for the Electroneutral Micro-Fluids. Advances in Applied Mathematics and Mechanics. 14 (2). 386-414. doi:10.4208/aamm.OA-2020-0327
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