A posteriori error estimates for the monodomain model in cardiac electrophysiology
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arXiv
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866929641084682240 |
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| author | Ratti, Luca Verani, Marco |
| author_facet | Ratti, Luca Verani, Marco |
| contents | We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_07468 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A posteriori error estimates for the monodomain model in cardiac electrophysiology Ratti, Luca Verani, Marco Numerical Analysis Analysis of PDEs We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplified) mathematical description of the electrical activity of the heart. We derive a posteriori error estimators accounting for different sources of error (space/time discretization and linearization). We prove reliability and efficiency (this latter under a suitable assumption) of the error indicators. Finally, numerical experiments assess the validity of the theoretical results. |
| title | A posteriori error estimates for the monodomain model in cardiac electrophysiology |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/1901.07468 |