Research Article
Open Access
A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation
1
Academician Expert Workstation, Hunan Sany Polytechnic College, Changsha 410129, China
2
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
* Corresponding Author:
Zhendong Luo,
[email protected]
Volume 1, Issue 1
2025
Received: 29 May 2025
Accepted: 28 June 2025
Published: 30 June 2025
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Article Information
Volume/Issue
Volume 1, Issue 1, 2025
Pages
42-53
Abstract
In this article, we mainly develop a new two-grid Crank-Nicolson (CN) mixed finite element (FE) (TGCNMFE) method for the convective FitzHugh-Nagumo equation. For the purpose, a new time semi-discrete CN mixed (TSDCNM) scheme is created, and the existence, steadiness, and estimates of errors for the TSDCNM solutions are attested. Thereafter, a new TGCNMFE method is developed, and the existence, steadiness, and estimates of errors for the TGCNMFE solutions are discussed. Lastly, the rightness of the procured theoretical results and the effectiveness of the TGCNMFE method are attested through several numerical experiments.
Keywords
two-grid Crank-Nicolson finite element method
the convective FitzHugh-Nagumo equation
time semi-discrete Crank-Nicolson scheme
existence and steadiness
error estimate
Data Availability Statement
Data will be made available on request.
Funding
This work was supported by the National Natural Science Foundation of China under Grant 11671106.
Conflicts of Interest
The author declares no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
References
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Cite This Article
APA Style
Luo, Z. (2025). A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation. Journal of Numerical Simulations in Physics and Mathematics, 1(1), 42–53. https://doi.org/10.62762/JNSPM.2025.522377
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TY - JOUR AU - Luo, Zhendong PY - 2025 DA - 2025/06/30 TI - A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation JO - Journal of Numerical Simulations in Physics and Mathematics T2 - Journal of Numerical Simulations in Physics and Mathematics JF - Journal of Numerical Simulations in Physics and Mathematics VL - 1 IS - 1 SP - 42 EP - 53 DO - 10.62762/JNSPM.2025.522377 UR - https://www.icck.org/article/abs/JNSPM.2025.522377 KW - two-grid Crank-Nicolson finite element method KW - the convective FitzHugh-Nagumo equation KW - time semi-discrete Crank-Nicolson scheme KW - existence and steadiness KW - error estimate AB - In this article, we mainly develop a new two-grid Crank-Nicolson (CN) mixed finite element (FE) (TGCNMFE) method for the convective FitzHugh-Nagumo equation. For the purpose, a new time semi-discrete CN mixed (TSDCNM) scheme is created, and the existence, steadiness, and estimates of errors for the TSDCNM solutions are attested. Thereafter, a new TGCNMFE method is developed, and the existence, steadiness, and estimates of errors for the TGCNMFE solutions are discussed. Lastly, the rightness of the procured theoretical results and the effectiveness of the TGCNMFE method are attested through several numerical experiments. SN - 3068-9082 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{Luo2025A,
author = {Zhendong Luo},
title = {A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation},
journal = {Journal of Numerical Simulations in Physics and Mathematics},
year = {2025},
volume = {1},
number = {1},
pages = {42-53},
doi = {10.62762/JNSPM.2025.522377},
url = {https://www.icck.org/article/abs/JNSPM.2025.522377},
abstract = {In this article, we mainly develop a new two-grid Crank-Nicolson (CN) mixed finite element (FE) (TGCNMFE) method for the convective FitzHugh-Nagumo equation. For the purpose, a new time semi-discrete CN mixed (TSDCNM) scheme is created, and the existence, steadiness, and estimates of errors for the TSDCNM solutions are attested. Thereafter, a new TGCNMFE method is developed, and the existence, steadiness, and estimates of errors for the TGCNMFE solutions are discussed. Lastly, the rightness of the procured theoretical results and the effectiveness of the TGCNMFE method are attested through several numerical experiments.},
keywords = {two-grid Crank-Nicolson finite element method, the convective FitzHugh-Nagumo equation, time semi-discrete Crank-Nicolson scheme, existence and steadiness, error estimate},
issn = {3068-9082},
publisher = {Institute of Central Computation and Knowledge}
}
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Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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