Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions
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....
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004315 |
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| author | S. Dawe M.S. Daoussa Haggar L.M. Kemfouet Tsopze M. Mbehou |
| author_facet | S. Dawe M.S. Daoussa Haggar L.M. Kemfouet Tsopze M. Mbehou |
| author_sort | S. Dawe |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4e7ee1679e2440dc9e5df8a2b965b4a4 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-4e7ee1679e2440dc9e5df8a2b965b4a42025-01-01T05:11:22ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101045Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditionsS. Dawe0M.S. Daoussa Haggar1L.M. Kemfouet Tsopze2M. Mbehou3Department of Mathematics, University of Ndjamena, ChadDepartment of Mathematics, University of Ndjamena, ChadDepartment of Mathematics, University of Yaounde I, CameroonDepartment of Mathematics, University of Yaounde I, Cameroon; Corresponding author.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.http://www.sciencedirect.com/science/article/pii/S2666818124004315Fitzhugh–Nagumo modelCrank–Nicolson methodNonlinear reaction–diffusionRobin boundaryError estimates |
| spellingShingle | S. Dawe M.S. Daoussa Haggar L.M. Kemfouet Tsopze M. Mbehou Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions Partial Differential Equations in Applied Mathematics Fitzhugh–Nagumo model Crank–Nicolson method Nonlinear reaction–diffusion Robin boundary Error estimates |
| title | Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| title_full | Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| title_fullStr | Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| title_full_unstemmed | Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| title_short | Error analysis of Crank–Nicolson-FEM for Fitzhugh–Nagumo system with Robin boundary conditions |
| title_sort | error analysis of crank nicolson fem for fitzhugh nagumo system with robin boundary conditions |
| topic | Fitzhugh–Nagumo model Crank–Nicolson method Nonlinear reaction–diffusion Robin boundary Error estimates |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004315 |
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