A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913295439495168 |
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| author | Burman, Erik Durst, Rebecca Fernández, Miguel A. Guzmán, Johnny Liu, Sijing |
| author_facet | Burman, Erik Durst, Rebecca Fernández, Miguel A. Guzmán, Johnny Liu, Sijing |
| contents | We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the correction step converge at $\mathcal O((Δt)^2)$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $Δt$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems Burman, Erik Durst, Rebecca Fernández, Miguel A. Guzmán, Johnny Liu, Sijing Numerical Analysis We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the correction step converge at $\mathcal O((Δt)^2)$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $Δt$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions. |
| title | A second-order correction method for loosely coupled discretizations applied to parabolic-parabolic interface problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.01599 |