A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation

Zhendong Luo

doi:10.62762/JNSPM.2025.522377

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Volume 1, Issue 1, Journal of Numerical Simulations in Physics and Mathematics

Volume 1, Issue 1, 2025

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Journal of Numerical Simulations in Physics and Mathematics, Volume 1, Issue 1, 2025: 42-53

Open Access | Research Article | 30 June 2025

A New Two-grid Crank-Nicolson Mixed Finite Element Method for Convective FitzHugh-Nagumo Equation

Zhendong Luo 1 *

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]

DOI: 10.62762/JNSPM.2025.522377

Received: 29 May 2025, Accepted: 28 June 2025, Published: 30 June 2025

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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.

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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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