| Title: |
Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| Authors: |
S. Dawe, M.S. Daoussa Haggar, L.M. Kemfouet Tsopze, M. Mbehou |
| Source: |
Partial Differential Equations in Applied Mathematics, Vol 13, Iss , Pp 101045- (2025) |
| Publisher Information: |
Elsevier, 2025. |
| Publication Year: |
2025 |
| Collection: |
LCC:Applied mathematics. Quantitative methods |
| Subject Terms: |
Fitzhugh–Nagumo model, Crank–Nicolson method, Nonlinear reaction–diffusion, Robin boundary, Error estimates, Applied mathematics. Quantitative methods, T57-57.97 |
| More Details: |
We investigate the convergence properties Crank–Nicolson scheme coupled with the finite element approximation of the Fitzhugh–Nagumo system. This model describes the dynamics of excitable media, such as nerve cells, and has applications in various fields, including neuroscience and cardiac modeling. The study focuses on the time splitting algorithm, which combines implicit time-stepping using Crank–Nicolson with piecewise finite element spatial discretization. The well-posedness and error estimates for both the temporal and fully discretization errors are established. This type of boundary conditions are incorporated into the formulation, allowing for non-homogeneous fluxes at the domain boundaries. Numerical experiments validate the theoretical findings. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2666-8181 |
| Relation: |
http://www.sciencedirect.com/science/article/pii/S2666818124004315; https://doaj.org/toc/2666-8181 |
| DOI: |
10.1016/j.padiff.2024.101045 |
| Access URL: |
https://doaj.org/article/4e7ee1679e2440dc9e5df8a2b965b4a4 |
| Accession Number: |
edsdoj.4e7ee1679e2440dc9e5df8a2b965b4a4 |
| Database: |
Directory of Open Access Journals |
