A second-order correction method for loosely coupled discretizations applied to parabolic–parabolic interface problems
Abstract 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 $\mathcal O((\varDelta t)^{2})$, under suitable convergence rate assumptions on the discrete time derivative of the prediction step, where $\varDelta t$ stands for the time-step length. Numerical results are shown to support our analysis and the assumptions.
Authors
- Erik Burman (ORCID: https://orcid.org/0000-0003-4287-7241)
- Sijing Liu (ORCID: https://orcid.org/0000-0001-6051-4482)
- Johnny Guzmán (ORCID: https://orcid.org/0000-0002-6769-2393)
- R. Durst (ORCID: https://orcid.org/0000-0001-9777-7171)
- Miguel Fernández Pérez (ORCID: https://orcid.org/0000-0003-0949-2104)
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Pittsburgh (US)
- Brown University (US)
- Sorbonne Université (FR)
- University College London (GB)
Publication Details
- Journal
- IMA Journal of Numerical Analysis
- Published
- 2024-09-13
- DOI
- https://doi.org/10.1093/imanum/drae075
- Citations
- 3
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 1.12
Funders
- National Science Foundation
- Engineering and Physical Sciences Research Council